Properties

Label 9633.2.a
Level $9633$
Weight $2$
Character orbit 9633.a
Rep. character $\chi_{9633}(1,\cdot)$
Character field $\Q$
Dimension $466$
Newform subspaces $49$
Sturm bound $2426$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 9633 = 3 \cdot 13^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9633.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 49 \)
Sturm bound: \(2426\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9633))\).

Total New Old
Modular forms 1240 466 774
Cusp forms 1185 466 719
Eisenstein series 55 0 55

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

\(3\)\(13\)\(19\)FrickeDim
\(+\)\(+\)\(+\)$+$\(60\)
\(+\)\(+\)\(-\)$-$\(53\)
\(+\)\(-\)\(+\)$-$\(57\)
\(+\)\(-\)\(-\)$+$\(63\)
\(-\)\(+\)\(+\)$-$\(67\)
\(-\)\(+\)\(-\)$+$\(46\)
\(-\)\(-\)\(+\)$+$\(51\)
\(-\)\(-\)\(-\)$-$\(69\)
Plus space\(+\)\(220\)
Minus space\(-\)\(246\)

Trace form

\( 466 q - 2 q^{2} + 464 q^{4} + 6 q^{5} - 2 q^{6} - 10 q^{7} - 6 q^{8} + 466 q^{9} + O(q^{10}) \) \( 466 q - 2 q^{2} + 464 q^{4} + 6 q^{5} - 2 q^{6} - 10 q^{7} - 6 q^{8} + 466 q^{9} + 8 q^{10} - 6 q^{11} + 8 q^{12} + 12 q^{14} - 4 q^{15} + 484 q^{16} + 18 q^{17} - 2 q^{18} - 4 q^{19} + 28 q^{20} + 8 q^{22} - 12 q^{23} + 6 q^{24} + 472 q^{25} - 36 q^{28} - 8 q^{29} - 4 q^{30} - 4 q^{31} - 14 q^{32} - 16 q^{33} + 32 q^{34} - 6 q^{35} + 464 q^{36} + 28 q^{40} + 28 q^{41} + 32 q^{42} + 14 q^{43} - 24 q^{44} + 6 q^{45} + 4 q^{46} + 14 q^{47} + 452 q^{49} + 38 q^{50} + 12 q^{51} - 2 q^{54} + 42 q^{55} + 48 q^{56} - 2 q^{57} - 8 q^{58} + 32 q^{59} + 8 q^{60} + 30 q^{61} + 64 q^{62} - 10 q^{63} + 500 q^{64} + 20 q^{66} + 12 q^{68} + 4 q^{69} + 44 q^{70} + 32 q^{71} - 6 q^{72} + 2 q^{73} - 60 q^{74} + 24 q^{75} - 10 q^{76} - 14 q^{77} + 16 q^{79} + 48 q^{80} + 466 q^{81} + 24 q^{82} + 12 q^{83} - 40 q^{84} - 2 q^{85} - 20 q^{86} + 12 q^{87} - 84 q^{88} + 8 q^{89} + 8 q^{90} + 28 q^{92} - 16 q^{93} + 8 q^{94} - 2 q^{95} + 30 q^{96} + 12 q^{97} + 34 q^{98} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9633))\) 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 13 19
9633.2.a.a 9633.a 1.a $1$ $76.920$ \(\Q\) None \(-2\) \(-1\) \(-2\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots\)
9633.2.a.b 9633.a 1.a $1$ $76.920$ \(\Q\) None \(-2\) \(1\) \(-4\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-4q^{5}-2q^{6}+\cdots\)
9633.2.a.c 9633.a 1.a $1$ $76.920$ \(\Q\) None \(-2\) \(1\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
9633.2.a.d 9633.a 1.a $1$ $76.920$ \(\Q\) None \(-2\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
9633.2.a.e 9633.a 1.a $1$ $76.920$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
9633.2.a.f 9633.a 1.a $1$ $76.920$ \(\Q\) None \(-1\) \(-1\) \(3\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
9633.2.a.g 9633.a 1.a $1$ $76.920$ \(\Q\) None \(-1\) \(1\) \(-3\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-3q^{5}-q^{6}-5q^{7}+\cdots\)
9633.2.a.h 9633.a 1.a $1$ $76.920$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+3q^{8}+\cdots\)
9633.2.a.i 9633.a 1.a $1$ $76.920$ \(\Q\) None \(0\) \(1\) \(-2\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-2q^{5}+3q^{7}+q^{9}-6q^{11}+\cdots\)
9633.2.a.j 9633.a 1.a $1$ $76.920$ \(\Q\) None \(0\) \(1\) \(-1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
9633.2.a.k 9633.a 1.a $1$ $76.920$ \(\Q\) None \(0\) \(1\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-3q^{7}+q^{9}-2q^{11}+\cdots\)
9633.2.a.l 9633.a 1.a $1$ $76.920$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+3q^{7}+q^{9}+2q^{11}+\cdots\)
9633.2.a.m 9633.a 1.a $1$ $76.920$ \(\Q\) None \(0\) \(1\) \(2\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+6q^{11}+\cdots\)
9633.2.a.n 9633.a 1.a $1$ $76.920$ \(\Q\) None \(2\) \(-1\) \(2\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots\)
9633.2.a.o 9633.a 1.a $1$ $76.920$ \(\Q\) None \(2\) \(-1\) \(3\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
9633.2.a.p 9633.a 1.a $1$ $76.920$ \(\Q\) None \(2\) \(1\) \(-1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-3q^{7}+\cdots\)
9633.2.a.q 9633.a 1.a $1$ $76.920$ \(\Q\) None \(2\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
9633.2.a.r 9633.a 1.a $1$ $76.920$ \(\Q\) None \(2\) \(1\) \(4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
9633.2.a.s 9633.a 1.a $2$ $76.920$ \(\Q(\sqrt{17}) \) None \(-1\) \(-2\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
9633.2.a.t 9633.a 1.a $2$ $76.920$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}+(3-\beta )q^{7}+\cdots\)
9633.2.a.u 9633.a 1.a $3$ $76.920$ 3.3.621.1 None \(0\) \(3\) \(3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
9633.2.a.v 9633.a 1.a $4$ $76.920$ 4.4.11324.1 None \(1\) \(-4\) \(4\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
9633.2.a.w 9633.a 1.a $5$ $76.920$ 5.5.2762272.1 None \(-1\) \(-5\) \(-3\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
9633.2.a.x 9633.a 1.a $5$ $76.920$ 5.5.504568.1 None \(1\) \(-5\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{2}+\beta _{4})q^{5}+\cdots\)
9633.2.a.y 9633.a 1.a $6$ $76.920$ 6.6.181100529.1 None \(-1\) \(6\) \(-4\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
9633.2.a.z 9633.a 1.a $6$ $76.920$ 6.6.181100529.1 None \(1\) \(6\) \(4\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
9633.2.a.ba 9633.a 1.a $9$ $76.920$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(-9\) \(-8\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{6}-\beta _{7})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots\)
9633.2.a.bb 9633.a 1.a $9$ $76.920$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(9\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
9633.2.a.bc 9633.a 1.a $9$ $76.920$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(-9\) \(8\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{6}-\beta _{7})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
9633.2.a.bd 9633.a 1.a $10$ $76.920$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-10\) \(-2\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
9633.2.a.be 9633.a 1.a $10$ $76.920$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(10\) \(-2\) \(-10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
9633.2.a.bf 9633.a 1.a $10$ $76.920$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(-10\) \(2\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
9633.2.a.bg 9633.a 1.a $10$ $76.920$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(10\) \(2\) \(10\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots\)
9633.2.a.bh 9633.a 1.a $11$ $76.920$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-2\) \(-11\) \(-4\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
9633.2.a.bi 9633.a 1.a $11$ $76.920$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-2\) \(11\) \(-4\) \(-10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
9633.2.a.bj 9633.a 1.a $11$ $76.920$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(2\) \(-11\) \(4\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
9633.2.a.bk 9633.a 1.a $11$ $76.920$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(2\) \(11\) \(4\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
9633.2.a.bl 9633.a 1.a $18$ $76.920$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-2\) \(18\) \(1\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+\beta _{16}q^{5}-\beta _{1}q^{6}+\cdots\)
9633.2.a.bm 9633.a 1.a $18$ $76.920$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(18\) \(-1\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-\beta _{16}q^{5}+\beta _{1}q^{6}+\cdots\)
9633.2.a.bn 9633.a 1.a $22$ $76.920$ None \(-4\) \(-22\) \(-8\) \(-12\) $+$ $-$ $-$ $\mathrm{SU}(2)$
9633.2.a.bo 9633.a 1.a $22$ $76.920$ None \(-4\) \(22\) \(-8\) \(-20\) $-$ $-$ $+$ $\mathrm{SU}(2)$
9633.2.a.bp 9633.a 1.a $22$ $76.920$ None \(4\) \(-22\) \(8\) \(12\) $+$ $-$ $+$ $\mathrm{SU}(2)$
9633.2.a.bq 9633.a 1.a $22$ $76.920$ None \(4\) \(22\) \(8\) \(20\) $-$ $-$ $-$ $\mathrm{SU}(2)$
9633.2.a.br 9633.a 1.a $24$ $76.920$ None \(-4\) \(-24\) \(1\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$
9633.2.a.bs 9633.a 1.a $24$ $76.920$ None \(4\) \(-24\) \(-1\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$
9633.2.a.bt 9633.a 1.a $30$ $76.920$ None \(-4\) \(-30\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$
9633.2.a.bu 9633.a 1.a $30$ $76.920$ None \(4\) \(-30\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$
9633.2.a.bv 9633.a 1.a $36$ $76.920$ None \(-2\) \(36\) \(2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$
9633.2.a.bw 9633.a 1.a $36$ $76.920$ None \(2\) \(36\) \(-2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9633))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9633)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(247))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(741))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3211))\)\(^{\oplus 2}\)