Properties

Label 637.2.k
Level $637$
Weight $2$
Character orbit 637.k
Rep. character $\chi_{637}(459,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $86$
Newform subspaces $10$
Sturm bound $130$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(130\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(637, [\chi])\).

Total New Old
Modular forms 146 102 44
Cusp forms 114 86 28
Eisenstein series 32 16 16

Trace form

\( 86 q + 2 q^{3} - 78 q^{4} + 6 q^{6} - 41 q^{9} + O(q^{10}) \) \( 86 q + 2 q^{3} - 78 q^{4} + 6 q^{6} - 41 q^{9} - 9 q^{10} - 3 q^{11} + 2 q^{12} + 4 q^{13} - 15 q^{15} + 58 q^{16} + 22 q^{17} + 51 q^{18} - 6 q^{19} + 6 q^{20} + 10 q^{23} - 18 q^{24} + 35 q^{25} - 6 q^{26} - 22 q^{27} - 2 q^{29} + 26 q^{30} - 15 q^{31} + 15 q^{33} + 37 q^{36} - 16 q^{38} - 21 q^{39} + 4 q^{40} + 15 q^{41} - 22 q^{43} - 48 q^{44} - 14 q^{48} + 30 q^{50} - 36 q^{51} + 5 q^{52} + 17 q^{53} + 24 q^{55} + 111 q^{58} + 129 q^{60} + 2 q^{61} - 38 q^{62} - 16 q^{64} - 70 q^{65} + 43 q^{66} - 54 q^{67} - 10 q^{68} - 7 q^{69} - 75 q^{71} - 159 q^{72} - 57 q^{73} - 6 q^{74} + 6 q^{75} + 42 q^{76} - 123 q^{78} + 6 q^{79} + 78 q^{80} - 23 q^{81} + 4 q^{82} - 9 q^{85} + 114 q^{86} + 26 q^{87} + 29 q^{88} + 12 q^{90} + 62 q^{92} + 14 q^{94} - 70 q^{95} - 12 q^{96} + 12 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(637, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
637.2.k.a 637.k 91.k $2$ $5.086$ \(\Q(\sqrt{-3}) \) None 13.2.e.a \(0\) \(-2\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}-2\zeta_{6}q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
637.2.k.b 637.k 91.k $2$ $5.086$ \(\Q(\sqrt{-3}) \) None 91.2.k.a \(0\) \(-1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{2}-\zeta_{6}q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
637.2.k.c 637.k 91.k $2$ $5.086$ \(\Q(\sqrt{-3}) \) None 13.2.e.a \(0\) \(2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}+2\zeta_{6}q^{3}-q^{4}+(2+\cdots)q^{5}+\cdots\)
637.2.k.d 637.k 91.k $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 637.2.q.e \(0\) \(-1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
637.2.k.e 637.k 91.k $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{-13})\) None 637.2.q.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\beta _{2})q^{2}-q^{4}+\beta _{1}q^{5}+(1-2\beta _{2}+\cdots)q^{8}+\cdots\)
637.2.k.f 637.k 91.k $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 637.2.q.e \(0\) \(1\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+2\beta _{1}+2\beta _{2}+\cdots)q^{3}+\cdots\)
637.2.k.g 637.k 91.k $12$ $5.086$ 12.0.\(\cdots\).1 None 91.2.q.a \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{4}+\beta _{8})q^{2}+(\beta _{2}+\beta _{9})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.k.h 637.k 91.k $12$ $5.086$ 12.0.\(\cdots\).1 None 91.2.q.a \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{4}+\beta _{8})q^{2}+(-\beta _{2}-\beta _{9})q^{3}+\cdots\)
637.2.k.i 637.k 91.k $12$ $5.086$ 12.0.\(\cdots\).1 None 91.2.k.b \(0\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{9}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.k.j 637.k 91.k $32$ $5.086$ None 637.2.q.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(637, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(637, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)