Properties

Label 4732.2.g
Level $4732$
Weight $2$
Character orbit 4732.g
Rep. character $\chi_{4732}(337,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $12$
Sturm bound $1456$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 4732 = 2^{2} \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4732.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1456\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4732, [\chi])\).

Total New Old
Modular forms 770 76 694
Cusp forms 686 76 610
Eisenstein series 84 0 84

Trace form

\( 76 q + 76 q^{9} + O(q^{10}) \) \( 76 q + 76 q^{9} - 4 q^{17} + 8 q^{23} - 84 q^{25} - 12 q^{27} - 8 q^{35} + 8 q^{43} - 76 q^{49} + 8 q^{51} - 24 q^{53} + 20 q^{55} - 8 q^{61} + 4 q^{69} + 20 q^{75} + 32 q^{79} + 124 q^{81} + 40 q^{87} + 16 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4732, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4732.2.g.a 4732.g 13.b $2$ $37.785$ \(\Q(\sqrt{-1}) \) None 364.2.a.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2 q^{3}+i q^{5}+i q^{7}+q^{9}+4 i q^{11}+\cdots\)
4732.2.g.b 4732.g 13.b $2$ $37.785$ \(\Q(\sqrt{-1}) \) None 364.2.k.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{5}+i q^{7}-3 q^{9}+2 i q^{11}+\cdots\)
4732.2.g.c 4732.g 13.b $2$ $37.785$ \(\Q(\sqrt{-1}) \) None 364.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{5}+i q^{7}-3 q^{9}-2 i q^{11}+\cdots\)
4732.2.g.d 4732.g 13.b $2$ $37.785$ \(\Q(\sqrt{-1}) \) None 364.2.k.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 i q^{5}+i q^{7}-3 q^{9}-2 i q^{11}+\cdots\)
4732.2.g.e 4732.g 13.b $4$ $37.785$ \(\Q(i, \sqrt{21})\) None 364.2.k.d \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+(2+\cdots)q^{9}+\cdots\)
4732.2.g.f 4732.g 13.b $4$ $37.785$ \(\Q(i, \sqrt{6})\) None 364.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
4732.2.g.g 4732.g 13.b $4$ $37.785$ \(\Q(i, \sqrt{13})\) None 364.2.k.c \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\beta _{3}q^{9}+\cdots\)
4732.2.g.h 4732.g 13.b $4$ $37.785$ \(\Q(\zeta_{12})\) None 364.2.a.d \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta_{3}+1)q^{3}+\beta_{2} q^{5}-\beta_1 q^{7}+\cdots\)
4732.2.g.i 4732.g 13.b $6$ $37.785$ 6.0.153664.1 None 4732.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{1}q^{5}+\beta _{5}q^{7}-3q^{9}+(3\beta _{1}-4\beta _{3}+\cdots)q^{11}+\cdots\)
4732.2.g.j 4732.g 13.b $12$ $37.785$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 4732.2.a.q \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{5}+\beta _{8})q^{3}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
4732.2.g.k 4732.g 13.b $16$ $37.785$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 364.2.u.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-\beta _{3}-\beta _{13})q^{5}+\beta _{3}q^{7}+\cdots\)
4732.2.g.l 4732.g 13.b $18$ $37.785$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 4732.2.a.u \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1}+\beta _{4})q^{3}-\beta _{12}q^{5}+\beta _{14}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4732, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4732, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2366, [\chi])\)\(^{\oplus 2}\)