Properties

Label 7623.2.a
Level $7623$
Weight $2$
Character orbit 7623.a
Rep. character $\chi_{7623}(1,\cdot)$
Character field $\Q$
Dimension $273$
Newform subspaces $81$
Sturm bound $2112$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7623.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 81 \)
Sturm bound: \(2112\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7623))\).

Total New Old
Modular forms 1104 273 831
Cusp forms 1009 273 736
Eisenstein series 95 0 95

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

\(3\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(26\)
\(+\)\(+\)\(-\)\(-\)\(30\)
\(+\)\(-\)\(+\)\(-\)\(34\)
\(+\)\(-\)\(-\)\(+\)\(20\)
\(-\)\(+\)\(+\)\(-\)\(41\)
\(-\)\(+\)\(-\)\(+\)\(40\)
\(-\)\(-\)\(+\)\(+\)\(37\)
\(-\)\(-\)\(-\)\(-\)\(45\)
Plus space\(+\)\(123\)
Minus space\(-\)\(150\)

Trace form

\( 273 q + q^{2} + 269 q^{4} + 6 q^{5} - q^{7} - 3 q^{8} + O(q^{10}) \) \( 273 q + q^{2} + 269 q^{4} + 6 q^{5} - q^{7} - 3 q^{8} + 6 q^{10} + 6 q^{13} - 3 q^{14} + 269 q^{16} + 14 q^{17} - 8 q^{19} - 6 q^{20} - 12 q^{23} + 287 q^{25} + 2 q^{26} - 3 q^{28} + 22 q^{29} - 8 q^{31} - 35 q^{32} + 2 q^{34} + 6 q^{35} + 6 q^{37} - 24 q^{38} + 6 q^{40} + 22 q^{41} + 12 q^{43} + 20 q^{46} - 12 q^{47} + 273 q^{49} - 65 q^{50} + 50 q^{52} + 10 q^{53} - 15 q^{56} + 34 q^{58} - 8 q^{59} + 18 q^{61} + 4 q^{62} + 309 q^{64} + 20 q^{65} + 4 q^{67} + 30 q^{68} + 18 q^{70} - 2 q^{73} + 22 q^{74} + 36 q^{76} - 36 q^{79} + 22 q^{80} + 38 q^{82} + 12 q^{83} + 16 q^{85} + 12 q^{86} + 26 q^{89} - 6 q^{91} - 20 q^{92} - 36 q^{94} - 20 q^{95} - 14 q^{97} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7623))\) 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 7 11
7623.2.a.a 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-2\) \(0\) \(-1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.b 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-2\) \(0\) \(-1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.c 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-2\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.d 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-2\) \(0\) \(3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+3q^{5}-q^{7}-6q^{10}+\cdots\)
7623.2.a.e 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots\)
7623.2.a.f 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}-q^{7}+3q^{8}-2q^{10}+\cdots\)
7623.2.a.g 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-1\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-2q^{10}+\cdots\)
7623.2.a.h 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-1\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{5}+q^{7}+3q^{8}-3q^{10}+\cdots\)
7623.2.a.i 7623.a 1.a $1$ $60.870$ \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{5}-q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.j 7623.a 1.a $1$ $60.870$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.k 7623.a 1.a $1$ $60.870$ \(\Q\) None \(0\) \(0\) \(3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}-q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.l 7623.a 1.a $1$ $60.870$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}+q^{7}-4q^{13}+4q^{16}+\cdots\)
7623.2.a.m 7623.a 1.a $1$ $60.870$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots\)
7623.2.a.n 7623.a 1.a $1$ $60.870$ \(\Q\) None \(1\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots\)
7623.2.a.o 7623.a 1.a $1$ $60.870$ \(\Q\) None \(1\) \(0\) \(3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+3q^{5}-q^{7}-3q^{8}+3q^{10}+\cdots\)
7623.2.a.p 7623.a 1.a $1$ $60.870$ \(\Q\) None \(2\) \(0\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.q 7623.a 1.a $1$ $60.870$ \(\Q\) None \(2\) \(0\) \(-1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.r 7623.a 1.a $1$ $60.870$ \(\Q\) None \(2\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.s 7623.a 1.a $1$ $60.870$ \(\Q\) None \(2\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+3q^{5}+q^{7}+6q^{10}+\cdots\)
7623.2.a.t 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}-q^{5}-q^{7}+\cdots\)
7623.2.a.u 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}-\beta q^{5}+q^{7}+\cdots\)
7623.2.a.v 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}-q^{7}+\cdots\)
7623.2.a.w 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+(-2+3\beta )q^{5}-q^{7}+3q^{8}+\cdots\)
7623.2.a.x 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(4\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
7623.2.a.y 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
7623.2.a.z 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.ba 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(3\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.bb 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(4\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
7623.2.a.bc 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bd 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+q^{7}-3q^{8}+\cdots\)
7623.2.a.be 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+q^{7}+(-4+\cdots)q^{8}+\cdots\)
7623.2.a.bf 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{21}) \) None \(-1\) \(0\) \(-6\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(3+\beta )q^{4}-3q^{5}-q^{7}+(-5+\cdots)q^{8}+\cdots\)
7623.2.a.bg 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-\beta q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots\)
7623.2.a.bh 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-\beta q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots\)
7623.2.a.bi 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+2\beta q^{5}-q^{7}-\beta q^{8}+\cdots\)
7623.2.a.bj 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+3q^{4}-\beta q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bk 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+3q^{4}+(-1+\beta )q^{5}+\cdots\)
7623.2.a.bl 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(4\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{4}+2q^{5}-q^{7}-\beta q^{8}+\cdots\)
7623.2.a.bm 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bn 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
7623.2.a.bo 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bp 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(3\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bq 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(4\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
7623.2.a.br 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(-2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}+3q^{8}+\cdots\)
7623.2.a.bs 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.bt 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}-q^{5}-q^{7}+(4+\beta )q^{8}+\cdots\)
7623.2.a.bu 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+(-2+3\beta )q^{5}+q^{7}-3q^{8}+\cdots\)
7623.2.a.bv 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(4\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(2+\beta )q^{5}+\cdots\)
7623.2.a.bw 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bx 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.by 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}-\beta q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bz 7623.a 1.a $3$ $60.870$ 3.3.568.1 None \(-2\) \(0\) \(-1\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(3+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
7623.2.a.ca 7623.a 1.a $3$ $60.870$ 3.3.316.1 None \(-1\) \(0\) \(-1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
7623.2.a.cb 7623.a 1.a $3$ $60.870$ 3.3.837.1 None \(0\) \(0\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
7623.2.a.cc 7623.a 1.a $3$ $60.870$ 3.3.316.1 None \(1\) \(0\) \(-1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
7623.2.a.cd 7623.a 1.a $3$ $60.870$ 3.3.229.1 None \(2\) \(0\) \(-4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
7623.2.a.ce 7623.a 1.a $3$ $60.870$ 3.3.568.1 None \(2\) \(0\) \(-1\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(3+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
7623.2.a.cf 7623.a 1.a $4$ $60.870$ 4.4.7488.1 None \(-2\) \(0\) \(-6\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
7623.2.a.cg 7623.a 1.a $4$ $60.870$ 4.4.7488.1 None \(-2\) \(0\) \(2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
7623.2.a.ch 7623.a 1.a $4$ $60.870$ 4.4.2525.1 None \(-2\) \(0\) \(6\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
7623.2.a.ci 7623.a 1.a $4$ $60.870$ 4.4.725.1 None \(-1\) \(0\) \(4\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+\cdots\)
7623.2.a.cj 7623.a 1.a $4$ $60.870$ \(\Q(\sqrt{2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{5}-q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{10}+\cdots\)
7623.2.a.ck 7623.a 1.a $4$ $60.870$ \(\Q(\sqrt{2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{5}+q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{10}+\cdots\)
7623.2.a.cl 7623.a 1.a $4$ $60.870$ 4.4.725.1 None \(1\) \(0\) \(4\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+2\beta _{2}q^{5}+\cdots\)
7623.2.a.cm 7623.a 1.a $4$ $60.870$ 4.4.7488.1 None \(2\) \(0\) \(-6\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
7623.2.a.cn 7623.a 1.a $4$ $60.870$ 4.4.7488.1 None \(2\) \(0\) \(2\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
7623.2.a.co 7623.a 1.a $4$ $60.870$ 4.4.2525.1 None \(2\) \(0\) \(6\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
7623.2.a.cp 7623.a 1.a $6$ $60.870$ 6.6.7674048.1 None \(-4\) \(0\) \(4\) \(6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
7623.2.a.cq 7623.a 1.a $6$ $60.870$ 6.6.3829849.1 None \(0\) \(0\) \(0\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
7623.2.a.cr 7623.a 1.a $6$ $60.870$ 6.6.3829849.1 None \(0\) \(0\) \(0\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
7623.2.a.cs 7623.a 1.a $6$ $60.870$ 6.6.7674048.1 None \(4\) \(0\) \(4\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
7623.2.a.ct 7623.a 1.a $8$ $60.870$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(0\) \(-10\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{5}+\beta _{6})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
7623.2.a.cu 7623.a 1.a $8$ $60.870$ 8.8.6988960000.1 None \(0\) \(0\) \(0\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{7})q^{5}-q^{7}+\cdots\)
7623.2.a.cv 7623.a 1.a $8$ $60.870$ 8.8.6988960000.1 None \(0\) \(0\) \(0\) \(8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots\)
7623.2.a.cw 7623.a 1.a $8$ $60.870$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(0\) \(-10\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{5}+\beta _{6})q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
7623.2.a.cx 7623.a 1.a $10$ $60.870$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-5\) \(-10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}-q^{7}+\cdots\)
7623.2.a.cy 7623.a 1.a $10$ $60.870$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-5\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}+q^{7}+\cdots\)
7623.2.a.cz 7623.a 1.a $12$ $60.870$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-12\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{8}q^{5}-q^{7}+\cdots\)
7623.2.a.da 7623.a 1.a $12$ $60.870$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(12\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+q^{7}+\cdots\)
7623.2.a.db 7623.a 1.a $16$ $60.870$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-16\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}-q^{7}+\cdots\)
7623.2.a.dc 7623.a 1.a $16$ $60.870$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(16\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7623))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7623)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\)\(^{\oplus 2}\)