Properties

Label 9075.2.a
Level $9075$
Weight $2$
Character orbit 9075.a
Rep. character $\chi_{9075}(1,\cdot)$
Character field $\Q$
Dimension $345$
Newform subspaces $105$
Sturm bound $2640$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9075.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 105 \)
Sturm bound: \(2640\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(2\), \(7\), \(13\), \(17\), \(19\), \(23\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9075))\).

Total New Old
Modular forms 1392 345 1047
Cusp forms 1249 345 904
Eisenstein series 143 0 143

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(36\)
\(+\)\(+\)\(-\)\(-\)\(45\)
\(+\)\(-\)\(+\)\(-\)\(46\)
\(+\)\(-\)\(-\)\(+\)\(45\)
\(-\)\(+\)\(+\)\(-\)\(48\)
\(-\)\(+\)\(-\)\(+\)\(35\)
\(-\)\(-\)\(+\)\(+\)\(38\)
\(-\)\(-\)\(-\)\(-\)\(52\)
Plus space\(+\)\(154\)
Minus space\(-\)\(191\)

Trace form

\( 345 q - 3 q^{2} + q^{3} + 341 q^{4} - q^{6} + 4 q^{7} - 15 q^{8} + 345 q^{9} + O(q^{10}) \) \( 345 q - 3 q^{2} + q^{3} + 341 q^{4} - q^{6} + 4 q^{7} - 15 q^{8} + 345 q^{9} + 7 q^{12} - 2 q^{13} + 345 q^{16} - 10 q^{17} - 3 q^{18} + 14 q^{19} + 10 q^{21} - 4 q^{23} - 9 q^{24} + 42 q^{26} + q^{27} + 4 q^{28} - 6 q^{29} - 10 q^{31} - 23 q^{32} - 10 q^{34} + 341 q^{36} + 2 q^{37} - 4 q^{38} + 16 q^{39} + 26 q^{41} - 16 q^{42} - 16 q^{46} - 8 q^{47} - q^{48} + 363 q^{49} + 6 q^{51} - 54 q^{52} - 30 q^{53} - q^{54} - 12 q^{56} + 16 q^{57} + 6 q^{58} + 4 q^{59} + 8 q^{61} + 32 q^{62} + 4 q^{63} + 341 q^{64} + 24 q^{67} + 50 q^{68} - 8 q^{69} + 12 q^{71} - 15 q^{72} - 14 q^{73} - 22 q^{74} + 44 q^{76} - 6 q^{78} + 4 q^{79} + 345 q^{81} + 14 q^{82} + 28 q^{83} + 24 q^{84} + 4 q^{86} + 2 q^{87} - 26 q^{89} + 70 q^{91} + 8 q^{92} + 44 q^{93} + 64 q^{94} - 9 q^{96} + 38 q^{97} + 77 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9075))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 11
9075.2.a.a 9075.a 1.a $1$ $72.464$ \(\Q\) None \(-2\) \(-1\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
9075.2.a.b 9075.a 1.a $1$ $72.464$ \(\Q\) None \(-2\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
9075.2.a.c 9075.a 1.a $1$ $72.464$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-4q^{7}+3q^{8}+\cdots\)
9075.2.a.d 9075.a 1.a $1$ $72.464$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-2q^{7}+3q^{8}+\cdots\)
9075.2.a.e 9075.a 1.a $1$ $72.464$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
9075.2.a.f 9075.a 1.a $1$ $72.464$ \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-4q^{7}+3q^{8}+\cdots\)
9075.2.a.g 9075.a 1.a $1$ $72.464$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
9075.2.a.h 9075.a 1.a $1$ $72.464$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
9075.2.a.i 9075.a 1.a $1$ $72.464$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{7}+q^{9}+2q^{12}-q^{13}+\cdots\)
9075.2.a.j 9075.a 1.a $1$ $72.464$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{7}+q^{9}+2q^{12}+2q^{13}+\cdots\)
9075.2.a.k 9075.a 1.a $1$ $72.464$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{7}+q^{9}+2q^{12}-2q^{13}+\cdots\)
9075.2.a.l 9075.a 1.a $1$ $72.464$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{12}+q^{13}+\cdots\)
9075.2.a.m 9075.a 1.a $1$ $72.464$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots\)
9075.2.a.n 9075.a 1.a $1$ $72.464$ \(\Q\) None \(1\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+2q^{7}-3q^{8}+\cdots\)
9075.2.a.o 9075.a 1.a $1$ $72.464$ \(\Q\) None \(1\) \(-1\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+4q^{7}-3q^{8}+\cdots\)
9075.2.a.p 9075.a 1.a $1$ $72.464$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
9075.2.a.q 9075.a 1.a $1$ $72.464$ \(\Q\) None \(1\) \(1\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+4q^{7}-3q^{8}+\cdots\)
9075.2.a.r 9075.a 1.a $1$ $72.464$ \(\Q\) None \(1\) \(1\) \(0\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+4q^{7}-3q^{8}+\cdots\)
9075.2.a.s 9075.a 1.a $1$ $72.464$ \(\Q\) None \(2\) \(1\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-3q^{7}+\cdots\)
9075.2.a.t 9075.a 1.a $1$ $72.464$ \(\Q\) None \(2\) \(1\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots\)
9075.2.a.u 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(-3\) \(2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.v 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.w 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.x 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.y 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.z 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.ba 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.bb 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bc 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bd 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.be 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bf 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{15}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+\beta q^{7}+q^{9}+2q^{12}+\cdots\)
9075.2.a.bg 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}-2\beta q^{7}+\cdots\)
9075.2.a.bh 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+2q^{7}-\beta q^{8}+\cdots\)
9075.2.a.bi 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}+2\beta q^{7}+\cdots\)
9075.2.a.bj 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-\beta q^{8}+\cdots\)
9075.2.a.bk 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+3q^{4}+\beta q^{6}-\beta q^{7}+\cdots\)
9075.2.a.bl 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+\beta q^{7}+q^{9}-2q^{12}+\cdots\)
9075.2.a.bm 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{15}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+\beta q^{7}+q^{9}-2q^{12}+\cdots\)
9075.2.a.bn 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-2\beta q^{7}+\cdots\)
9075.2.a.bo 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-2\beta q^{7}+\cdots\)
9075.2.a.bp 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-\beta q^{8}+q^{9}+\cdots\)
9075.2.a.bq 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-\beta q^{8}+\cdots\)
9075.2.a.br 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-\beta q^{7}+\cdots\)
9075.2.a.bs 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bt 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bu 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bv 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
9075.2.a.bw 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.bx 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.by 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.bz 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
9075.2.a.ca 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.cb 9075.a 1.a $2$ $72.464$ \(\Q(\sqrt{5}) \) None \(3\) \(2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
9075.2.a.cc 9075.a 1.a $3$ $72.464$ 3.3.148.1 None \(-3\) \(-3\) \(0\) \(-8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9075.2.a.cd 9075.a 1.a $3$ $72.464$ 3.3.568.1 None \(-2\) \(3\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(3+\beta _{2})q^{4}+\cdots\)
9075.2.a.ce 9075.a 1.a $3$ $72.464$ 3.3.469.1 None \(-1\) \(-3\) \(0\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.cf 9075.a 1.a $3$ $72.464$ 3.3.148.1 None \(-1\) \(-3\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.cg 9075.a 1.a $3$ $72.464$ 3.3.148.1 None \(-1\) \(3\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.ch 9075.a 1.a $3$ $72.464$ 3.3.148.1 None \(1\) \(-3\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.ci 9075.a 1.a $3$ $72.464$ 3.3.469.1 None \(1\) \(-3\) \(0\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.cj 9075.a 1.a $3$ $72.464$ 3.3.568.1 None \(2\) \(-3\) \(0\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
9075.2.a.ck 9075.a 1.a $3$ $72.464$ 3.3.148.1 None \(3\) \(3\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9075.2.a.cl 9075.a 1.a $4$ $72.464$ 4.4.725.1 None \(-5\) \(-4\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1}+\beta _{2})q^{2}-q^{3}+(3-\beta _{1}+\cdots)q^{4}+\cdots\)
9075.2.a.cm 9075.a 1.a $4$ $72.464$ 4.4.725.1 None \(-3\) \(-4\) \(0\) \(-6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9075.2.a.cn 9075.a 1.a $4$ $72.464$ 4.4.5725.1 None \(-1\) \(-4\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.co 9075.a 1.a $4$ $72.464$ \(\Q(\zeta_{15})^+\) None \(-1\) \(4\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots\)
9075.2.a.cp 9075.a 1.a $4$ $72.464$ 4.4.5725.1 None \(-1\) \(4\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.cq 9075.a 1.a $4$ $72.464$ 4.4.5725.1 None \(-1\) \(4\) \(0\) \(8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.cr 9075.a 1.a $4$ $72.464$ \(\Q(\zeta_{24})^+\) None \(0\) \(-4\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-q^{3}-\beta _{2}q^{6}-\beta _{1}q^{7}-2\beta _{2}q^{8}+\cdots\)
9075.2.a.cs 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(-4\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}-2\beta _{3}q^{7}+\cdots\)
9075.2.a.ct 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(-4\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots\)
9075.2.a.cu 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(-4\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots\)
9075.2.a.cv 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(-4\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.cw 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(-4\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.cx 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{5})\) None \(0\) \(-4\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}-q^{3}+(2+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
9075.2.a.cy 9075.a 1.a $4$ $72.464$ \(\Q(\zeta_{24})^+\) None \(0\) \(4\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+\beta _{2}q^{6}-\beta _{1}q^{7}-2\beta _{2}q^{8}+\cdots\)
9075.2.a.cz 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(4\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+q^{3}-\beta _{2}q^{4}+\beta _{3}q^{6}-2\beta _{3}q^{7}+\cdots\)
9075.2.a.da 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(4\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+q^{3}-\beta _{2}q^{4}+\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots\)
9075.2.a.db 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{3})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dc 9075.a 1.a $4$ $72.464$ 4.4.8112.1 None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(2-\beta _{3})q^{4}-\beta _{2}q^{6}+\cdots\)
9075.2.a.dd 9075.a 1.a $4$ $72.464$ \(\Q(\sqrt{3}, \sqrt{5})\) None \(0\) \(4\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}+q^{3}+(2+\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
9075.2.a.de 9075.a 1.a $4$ $72.464$ 4.4.5725.1 None \(1\) \(-4\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.df 9075.a 1.a $4$ $72.464$ \(\Q(\zeta_{15})^+\) None \(1\) \(4\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{2}-\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
9075.2.a.dg 9075.a 1.a $4$ $72.464$ 4.4.5725.1 None \(1\) \(4\) \(0\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.dh 9075.a 1.a $4$ $72.464$ 4.4.5725.1 None \(1\) \(4\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{2})q^{2}+q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
9075.2.a.di 9075.a 1.a $4$ $72.464$ 4.4.725.1 None \(3\) \(-4\) \(0\) \(6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9075.2.a.dj 9075.a 1.a $4$ $72.464$ 4.4.725.1 None \(5\) \(-4\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1}-\beta _{2})q^{2}-q^{3}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
9075.2.a.dk 9075.a 1.a $5$ $72.464$ 5.5.9444552.1 None \(-1\) \(-5\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dl 9075.a 1.a $5$ $72.464$ 5.5.9444552.1 None \(-1\) \(5\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dm 9075.a 1.a $5$ $72.464$ 5.5.9444552.1 None \(1\) \(-5\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dn 9075.a 1.a $5$ $72.464$ 5.5.9444552.1 None \(1\) \(5\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.do 9075.a 1.a $6$ $72.464$ 6.6.860280160.1 None \(-1\) \(-6\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dp 9075.a 1.a $6$ $72.464$ 6.6.860280160.1 None \(-1\) \(6\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dq 9075.a 1.a $6$ $72.464$ 6.6.437199552.1 None \(0\) \(6\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dr 9075.a 1.a $6$ $72.464$ 6.6.860280160.1 None \(1\) \(-6\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.ds 9075.a 1.a $6$ $72.464$ 6.6.860280160.1 None \(1\) \(6\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dt 9075.a 1.a $8$ $72.464$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(-8\) \(0\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.du 9075.a 1.a $8$ $72.464$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(8\) \(0\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dv 9075.a 1.a $8$ $72.464$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-8\) \(0\) \(8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dw 9075.a 1.a $8$ $72.464$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(8\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dx 9075.a 1.a $12$ $72.464$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-12\) \(0\) \(-8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
9075.2.a.dy 9075.a 1.a $12$ $72.464$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(12\) \(0\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.dz 9075.a 1.a $12$ $72.464$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(-12\) \(0\) \(8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
9075.2.a.ea 9075.a 1.a $12$ $72.464$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(12\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9075))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9075)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1815))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3025))\)\(^{\oplus 2}\)