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Properties

Label 8050.2.a
Level $8050$
Weight $2$
Character orbit 8050.a
Rep. character $\chi_{8050}(1,\cdot)$
Character field $\Q$
Dimension $208$
Newform subspaces $62$
Sturm bound $2880$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 8050 = 2 \cdot 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8050.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 62 \)
Sturm bound: \(2880\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8050))\).

Total New Old
Modular forms 1464 208 1256
Cusp forms 1417 208 1209
Eisenstein series 47 0 47

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

\(2\)\(5\)\(7\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(12\)
\(+\)\(+\)\(+\)\(-\)$-$\(12\)
\(+\)\(+\)\(-\)\(+\)$-$\(13\)
\(+\)\(+\)\(-\)\(-\)$+$\(11\)
\(+\)\(-\)\(+\)\(+\)$-$\(12\)
\(+\)\(-\)\(+\)\(-\)$+$\(16\)
\(+\)\(-\)\(-\)\(+\)$+$\(14\)
\(+\)\(-\)\(-\)\(-\)$-$\(14\)
\(-\)\(+\)\(+\)\(+\)$-$\(15\)
\(-\)\(+\)\(+\)\(-\)$+$\(11\)
\(-\)\(+\)\(-\)\(+\)$+$\(10\)
\(-\)\(+\)\(-\)\(-\)$-$\(16\)
\(-\)\(-\)\(+\)\(+\)$+$\(11\)
\(-\)\(-\)\(+\)\(-\)$-$\(15\)
\(-\)\(-\)\(-\)\(+\)$-$\(17\)
\(-\)\(-\)\(-\)\(-\)$+$\(9\)
Plus space\(+\)\(94\)
Minus space\(-\)\(114\)

Trace form

\( 208 q + 4 q^{3} + 208 q^{4} + 4 q^{6} + 200 q^{9} + O(q^{10}) \) \( 208 q + 4 q^{3} + 208 q^{4} + 4 q^{6} + 200 q^{9} - 4 q^{11} + 4 q^{12} - 12 q^{13} + 208 q^{16} + 12 q^{19} - 8 q^{21} + 12 q^{22} + 4 q^{24} + 28 q^{26} + 16 q^{27} + 8 q^{29} + 16 q^{31} + 32 q^{34} + 200 q^{36} + 4 q^{37} - 20 q^{38} - 16 q^{39} + 40 q^{41} + 36 q^{43} - 4 q^{44} - 4 q^{46} - 40 q^{47} + 4 q^{48} + 208 q^{49} + 16 q^{51} - 12 q^{52} - 20 q^{53} + 40 q^{54} - 64 q^{57} - 8 q^{58} + 36 q^{59} + 12 q^{61} + 208 q^{64} + 56 q^{66} - 28 q^{67} - 32 q^{71} - 8 q^{73} + 28 q^{74} + 12 q^{76} - 8 q^{77} - 16 q^{79} + 224 q^{81} - 16 q^{82} + 4 q^{83} - 8 q^{84} + 44 q^{86} + 64 q^{87} + 12 q^{88} + 32 q^{89} - 24 q^{91} + 40 q^{93} + 24 q^{94} + 4 q^{96} - 32 q^{97} + 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8050))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 7 23
8050.2.a.a 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(-2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots\)
8050.2.a.b 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(-2\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots\)
8050.2.a.c 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
8050.2.a.d 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
8050.2.a.e 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{9}+6q^{13}+\cdots\)
8050.2.a.f 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-4q^{11}+\cdots\)
8050.2.a.g 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-4q^{11}+\cdots\)
8050.2.a.h 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}-2q^{11}+\cdots\)
8050.2.a.i 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots\)
8050.2.a.j 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
8050.2.a.k 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
8050.2.a.l 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{7}-q^{8}+\cdots\)
8050.2.a.m 8050.a 1.a $1$ $64.280$ \(\Q\) None \(-1\) \(2\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots\)
8050.2.a.n 8050.a 1.a $1$ $64.280$ \(\Q\) None \(1\) \(-2\) \(0\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
8050.2.a.o 8050.a 1.a $1$ $64.280$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-4q^{11}+\cdots\)
8050.2.a.p 8050.a 1.a $1$ $64.280$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}-4q^{11}+\cdots\)
8050.2.a.q 8050.a 1.a $1$ $64.280$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{9}+4q^{11}+\cdots\)
8050.2.a.r 8050.a 1.a $1$ $64.280$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{9}-4q^{13}+\cdots\)
8050.2.a.s 8050.a 1.a $1$ $64.280$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
8050.2.a.t 8050.a 1.a $1$ $64.280$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
8050.2.a.u 8050.a 1.a $1$ $64.280$ \(\Q\) None \(1\) \(2\) \(0\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots\)
8050.2.a.v 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
8050.2.a.w 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{17}) \) None \(-2\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+q^{7}-q^{8}+\cdots\)
8050.2.a.x 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{6}+\cdots\)
8050.2.a.y 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{21}) \) None \(-2\) \(4\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots\)
8050.2.a.z 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{21}) \) None \(2\) \(-4\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
8050.2.a.ba 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
8050.2.a.bb 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
8050.2.a.bc 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{17}) \) None \(2\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}-q^{7}+q^{8}+\cdots\)
8050.2.a.bd 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
8050.2.a.be 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
8050.2.a.bf 8050.a 1.a $2$ $64.280$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
8050.2.a.bg 8050.a 1.a $3$ $64.280$ 3.3.148.1 None \(-3\) \(-4\) \(0\) \(-3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
8050.2.a.bh 8050.a 1.a $3$ $64.280$ 3.3.316.1 None \(-3\) \(-2\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
8050.2.a.bi 8050.a 1.a $3$ $64.280$ 3.3.148.1 None \(-3\) \(2\) \(0\) \(-3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{6}+\cdots\)
8050.2.a.bj 8050.a 1.a $3$ $64.280$ 3.3.404.1 None \(-3\) \(2\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
8050.2.a.bk 8050.a 1.a $3$ $64.280$ 3.3.564.1 None \(3\) \(-2\) \(0\) \(-3\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
8050.2.a.bl 8050.a 1.a $3$ $64.280$ 3.3.148.1 None \(3\) \(-2\) \(0\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
8050.2.a.bm 8050.a 1.a $3$ $64.280$ 3.3.148.1 None \(3\) \(-2\) \(0\) \(3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{6}+\cdots\)
8050.2.a.bn 8050.a 1.a $3$ $64.280$ 3.3.316.1 None \(3\) \(2\) \(0\) \(-3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1+\beta _{2})q^{6}+\cdots\)
8050.2.a.bo 8050.a 1.a $4$ $64.280$ 4.4.25492.1 None \(-4\) \(0\) \(0\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{7}+\cdots\)
8050.2.a.bp 8050.a 1.a $4$ $64.280$ 4.4.63796.1 None \(4\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{7}+\cdots\)
8050.2.a.bq 8050.a 1.a $4$ $64.280$ 4.4.25492.1 None \(4\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{7}+\cdots\)
8050.2.a.br 8050.a 1.a $5$ $64.280$ 5.5.1933264.1 None \(-5\) \(0\) \(0\) \(-5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{6}+\cdots\)
8050.2.a.bs 8050.a 1.a $5$ $64.280$ 5.5.3035380.1 None \(-5\) \(0\) \(0\) \(5\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{3}q^{6}+q^{7}+\cdots\)
8050.2.a.bt 8050.a 1.a $5$ $64.280$ 5.5.126032.1 None \(-5\) \(2\) \(0\) \(-5\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{3}q^{6}-q^{7}+\cdots\)
8050.2.a.bu 8050.a 1.a $5$ $64.280$ 5.5.940784.1 None \(-5\) \(2\) \(0\) \(-5\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{7}+\cdots\)
8050.2.a.bv 8050.a 1.a $5$ $64.280$ 5.5.126032.1 None \(5\) \(-2\) \(0\) \(5\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{3}q^{6}+q^{7}+\cdots\)
8050.2.a.bw 8050.a 1.a $5$ $64.280$ 5.5.940784.1 None \(5\) \(-2\) \(0\) \(5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{7}+\cdots\)
8050.2.a.bx 8050.a 1.a $5$ $64.280$ 5.5.1933264.1 None \(5\) \(0\) \(0\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
8050.2.a.by 8050.a 1.a $6$ $64.280$ 6.6.244918864.1 None \(-6\) \(-3\) \(0\) \(6\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)
8050.2.a.bz 8050.a 1.a $6$ $64.280$ 6.6.244918864.1 None \(6\) \(3\) \(0\) \(-6\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1})q^{6}+\cdots\)
8050.2.a.ca 8050.a 1.a $7$ $64.280$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-2\) \(0\) \(7\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{7}+\cdots\)
8050.2.a.cb 8050.a 1.a $7$ $64.280$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(0\) \(0\) \(-7\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{7}+\cdots\)
8050.2.a.cc 8050.a 1.a $7$ $64.280$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(4\) \(0\) \(7\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
8050.2.a.cd 8050.a 1.a $7$ $64.280$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(-4\) \(0\) \(-7\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{6}+\cdots\)
8050.2.a.ce 8050.a 1.a $7$ $64.280$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(0\) \(0\) \(7\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{7}+\cdots\)
8050.2.a.cf 8050.a 1.a $7$ $64.280$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(2\) \(0\) \(-7\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{7}+\cdots\)
8050.2.a.cg 8050.a 1.a $9$ $64.280$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-2\) \(0\) \(9\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{7}+\cdots\)
8050.2.a.ch 8050.a 1.a $9$ $64.280$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(2\) \(0\) \(-9\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{7}+\cdots\)
8050.2.a.ci 8050.a 1.a $11$ $64.280$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-4\) \(0\) \(-11\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{7}+\cdots\)
8050.2.a.cj 8050.a 1.a $11$ $64.280$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(4\) \(0\) \(11\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8050))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8050)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(805))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1610))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\)\(^{\oplus 2}\)