Properties

Label 9610.2.a
Level $9610$
Weight $2$
Character orbit 9610.a
Rep. character $\chi_{9610}(1,\cdot)$
Character field $\Q$
Dimension $311$
Newform subspaces $63$
Sturm bound $2976$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 9610 = 2 \cdot 5 \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9610.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 63 \)
Sturm bound: \(2976\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9610))\).

Total New Old
Modular forms 1552 311 1241
Cusp forms 1425 311 1114
Eisenstein series 127 0 127

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

\(2\)\(5\)\(31\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(43\)
\(+\)\(+\)\(-\)\(-\)\(35\)
\(+\)\(-\)\(+\)\(-\)\(43\)
\(+\)\(-\)\(-\)\(+\)\(35\)
\(-\)\(+\)\(+\)\(-\)\(43\)
\(-\)\(+\)\(-\)\(+\)\(35\)
\(-\)\(-\)\(+\)\(+\)\(27\)
\(-\)\(-\)\(-\)\(-\)\(50\)
Plus space\(+\)\(140\)
Minus space\(-\)\(171\)

Trace form

\( 311 q - q^{2} + 311 q^{4} - q^{5} - 4 q^{6} + 8 q^{7} - q^{8} + 307 q^{9} + O(q^{10}) \) \( 311 q - q^{2} + 311 q^{4} - q^{5} - 4 q^{6} + 8 q^{7} - q^{8} + 307 q^{9} - q^{10} - 4 q^{11} + 14 q^{13} - 4 q^{15} + 311 q^{16} + 6 q^{17} + 3 q^{18} - 4 q^{19} - q^{20} + 16 q^{21} + 16 q^{23} - 4 q^{24} + 311 q^{25} + 10 q^{26} + 8 q^{28} - 14 q^{29} - q^{32} + 8 q^{33} - 10 q^{34} + 307 q^{36} + 14 q^{37} + 4 q^{38} - 8 q^{39} - q^{40} + 22 q^{41} - 8 q^{42} + 24 q^{43} - 4 q^{44} + 3 q^{45} + 8 q^{46} - 32 q^{47} + 303 q^{49} - q^{50} + 32 q^{51} + 14 q^{52} + 30 q^{53} - 16 q^{54} - 4 q^{55} + 8 q^{57} + 14 q^{58} - 20 q^{59} - 4 q^{60} + 18 q^{61} + 40 q^{63} + 311 q^{64} - 6 q^{65} + 40 q^{66} + 20 q^{67} + 6 q^{68} - 24 q^{69} - 8 q^{70} + 8 q^{71} + 3 q^{72} + 14 q^{73} + 2 q^{74} - 4 q^{76} - 8 q^{77} + 48 q^{78} - 32 q^{79} - q^{80} + 367 q^{81} - 10 q^{82} - 24 q^{83} + 16 q^{84} - 6 q^{85} + 12 q^{86} + 24 q^{87} + 6 q^{89} + 3 q^{90} - 8 q^{91} + 16 q^{92} - 4 q^{95} - 4 q^{96} + 14 q^{97} + 7 q^{98} - 20 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9610))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 31
9610.2.a.a 9610.a 1.a $1$ $76.736$ \(\Q\) None 310.2.a.b \(1\) \(-2\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots\)
9610.2.a.b 9610.a 1.a $1$ $76.736$ \(\Q\) None 310.2.a.a \(1\) \(2\) \(-1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)
9610.2.a.c 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{5}) \) None 310.2.h.a \(-2\) \(-2\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
9610.2.a.d 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{5}) \) None 310.2.h.b \(-2\) \(-2\) \(2\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
9610.2.a.e 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.e \(-2\) \(0\) \(-2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-2q^{7}+\cdots\)
9610.2.a.f 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{6}) \) None 310.2.a.d \(-2\) \(0\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-2q^{7}+\cdots\)
9610.2.a.g 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.g \(-2\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots\)
9610.2.a.h 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.h \(-2\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2\beta q^{3}+q^{4}+q^{5}-2\beta q^{6}+\cdots\)
9610.2.a.i 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.i \(-2\) \(0\) \(2\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+2q^{7}+\cdots\)
9610.2.a.j 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{3}) \) None 310.2.a.c \(-2\) \(2\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
9610.2.a.k 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{5}) \) None 310.2.h.a \(-2\) \(2\) \(2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
9610.2.a.l 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{5}) \) None 310.2.h.b \(-2\) \(2\) \(2\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
9610.2.a.m 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.m \(2\) \(0\) \(-2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-2q^{7}+\cdots\)
9610.2.a.n 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.n \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots\)
9610.2.a.o 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.o \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+q^{8}+\cdots\)
9610.2.a.p 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.p \(2\) \(0\) \(2\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-4q^{7}+\cdots\)
9610.2.a.q 9610.a 1.a $3$ $76.736$ 3.3.4065.1 None 310.2.e.b \(-3\) \(-1\) \(-3\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
9610.2.a.r 9610.a 1.a $3$ $76.736$ 3.3.321.1 None 310.2.e.a \(-3\) \(-1\) \(3\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots\)
9610.2.a.s 9610.a 1.a $3$ $76.736$ 3.3.4065.1 None 310.2.e.b \(-3\) \(1\) \(-3\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.t 9610.a 1.a $3$ $76.736$ 3.3.321.1 None 310.2.e.a \(-3\) \(1\) \(3\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
9610.2.a.u 9610.a 1.a $3$ $76.736$ 3.3.148.1 None 310.2.a.e \(3\) \(-2\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9610.2.a.v 9610.a 1.a $3$ $76.736$ 3.3.321.1 None 310.2.e.c \(3\) \(-1\) \(-3\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.w 9610.a 1.a $3$ $76.736$ 3.3.169.1 None 310.2.e.d \(3\) \(-1\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.x 9610.a 1.a $3$ $76.736$ 3.3.321.1 None 310.2.e.c \(3\) \(1\) \(-3\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
9610.2.a.y 9610.a 1.a $3$ $76.736$ 3.3.169.1 None 310.2.e.d \(3\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
9610.2.a.z 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.e \(-4\) \(-6\) \(-4\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-2-\beta _{3})q^{3}+q^{4}-q^{5}+(2+\cdots)q^{6}+\cdots\)
9610.2.a.ba 9610.a 1.a $4$ $76.736$ \(\Q(\sqrt{2}, \sqrt{5})\) None 310.2.h.e \(-4\) \(-4\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
9610.2.a.bb 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.f \(-4\) \(-4\) \(-4\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{3}+q^{4}+\cdots\)
9610.2.a.bc 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.d \(-4\) \(-2\) \(-4\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
9610.2.a.bd 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bd \(-4\) \(0\) \(-4\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.be 9610.a 1.a $4$ $76.736$ \(\Q(\sqrt{2}, \sqrt{5})\) None 9610.2.a.be \(-4\) \(0\) \(-4\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.bf 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bf \(-4\) \(0\) \(-4\) \(8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{1}+\beta _{3})q^{3}+q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
9610.2.a.bg 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.d \(-4\) \(2\) \(-4\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
9610.2.a.bh 9610.a 1.a $4$ $76.736$ \(\Q(\sqrt{2}, \sqrt{5})\) None 310.2.h.e \(-4\) \(4\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
9610.2.a.bi 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.f \(-4\) \(4\) \(-4\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
9610.2.a.bj 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.e \(-4\) \(6\) \(-4\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(2+\beta _{3})q^{3}+q^{4}-q^{5}+(-2+\cdots)q^{6}+\cdots\)
9610.2.a.bk 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.c \(4\) \(-4\) \(4\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{3}+q^{4}+\cdots\)
9610.2.a.bl 9610.a 1.a $4$ $76.736$ \(\Q(\sqrt{2}, \sqrt{5})\) None 310.2.h.d \(4\) \(-4\) \(4\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9610.2.a.bm 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.a \(4\) \(-2\) \(4\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
9610.2.a.bn 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.b \(4\) \(-2\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+q^{5}+\beta _{3}q^{6}+\cdots\)
9610.2.a.bo 9610.a 1.a $4$ $76.736$ 4.4.4400.1 None 310.2.h.c \(4\) \(0\) \(-4\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}-q^{5}-\beta _{3}q^{6}+\cdots\)
9610.2.a.bp 9610.a 1.a $4$ $76.736$ 4.4.4400.1 None 310.2.h.c \(4\) \(0\) \(-4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}-q^{5}-\beta _{3}q^{6}+\cdots\)
9610.2.a.bq 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bq \(4\) \(0\) \(4\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(\beta _{1}+\beta _{3})q^{3}+q^{4}+q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots\)
9610.2.a.br 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.br \(4\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{2}+\beta _{3})q^{3}+q^{4}+q^{5}+\cdots\)
9610.2.a.bs 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bs \(4\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9610.2.a.bt 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.br \(4\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+q^{5}+(\beta _{2}+\cdots)q^{6}+\cdots\)
9610.2.a.bu 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bu \(4\) \(0\) \(4\) \(16\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(\beta _{1}+2\beta _{3})q^{3}+q^{4}+q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots\)
9610.2.a.bv 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.a \(4\) \(2\) \(4\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
9610.2.a.bw 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.b \(4\) \(2\) \(4\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}+q^{5}-\beta _{3}q^{6}+\cdots\)
9610.2.a.bx 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.c \(4\) \(4\) \(4\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
9610.2.a.by 9610.a 1.a $4$ $76.736$ \(\Q(\sqrt{2}, \sqrt{5})\) None 310.2.h.d \(4\) \(4\) \(4\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{3})q^{3}+q^{4}+q^{5}+(1+\beta _{3})q^{6}+\cdots\)
9610.2.a.bz 9610.a 1.a $6$ $76.736$ 6.6.14623232.1 None 9610.2.a.bz \(6\) \(0\) \(6\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots\)
9610.2.a.ca 9610.a 1.a $8$ $76.736$ \(\Q(\zeta_{32})^+\) None 9610.2.a.ca \(-8\) \(0\) \(-8\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-\beta _{1}+\beta _{5}-\beta _{7})q^{3}+q^{4}+\cdots\)
9610.2.a.cb 9610.a 1.a $8$ $76.736$ 8.8.4848615424.1 None 9610.2.a.cb \(-8\) \(0\) \(8\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{3}-\beta _{7})q^{3}+q^{4}+q^{5}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
9610.2.a.cc 9610.a 1.a $8$ $76.736$ 8.8.\(\cdots\).1 None 9610.2.a.cc \(8\) \(0\) \(-8\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{4}q^{3}+q^{4}-q^{5}+\beta _{4}q^{6}+\cdots\)
9610.2.a.cd 9610.a 1.a $8$ $76.736$ \(\Q(\zeta_{32})^+\) None 9610.2.a.cd \(8\) \(0\) \(8\) \(-16\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{5}q^{3}+q^{4}+q^{5}-\beta _{5}q^{6}+\cdots\)
9610.2.a.ce 9610.a 1.a $12$ $76.736$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 310.2.q.h \(-12\) \(-4\) \(12\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9610.2.a.cf 9610.a 1.a $12$ $76.736$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 310.2.q.h \(-12\) \(4\) \(12\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.cg 9610.a 1.a $12$ $76.736$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 310.2.q.g \(12\) \(-4\) \(-12\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{6}q^{3}+q^{4}-q^{5}+\beta _{6}q^{6}+\cdots\)
9610.2.a.ch 9610.a 1.a $12$ $76.736$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 310.2.q.g \(12\) \(4\) \(-12\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{6}q^{3}+q^{4}-q^{5}-\beta _{6}q^{6}+\cdots\)
9610.2.a.ci 9610.a 1.a $16$ $76.736$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 9610.2.a.ci \(-16\) \(0\) \(-16\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{11}q^{3}+q^{4}-q^{5}-\beta _{11}q^{6}+\cdots\)
9610.2.a.cj 9610.a 1.a $24$ $76.736$ None 9610.2.a.cj \(-24\) \(0\) \(24\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$
9610.2.a.ck 9610.a 1.a $24$ $76.736$ None 9610.2.a.ck \(24\) \(0\) \(-24\) \(16\) $-$ $+$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9610)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(961))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1922))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4805))\)\(^{\oplus 2}\)