Properties

Label 637.2.q
Level $637$
Weight $2$
Character orbit 637.q
Rep. character $\chi_{637}(491,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $86$
Newform subspaces $10$
Sturm bound $130$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 10 \)
Sturm bound: \(130\)
Trace bound: \(3\)
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 148 106 42
Cusp forms 116 86 30
Eisenstein series 32 20 12

Trace form

\( 86 q + 3 q^{2} + 2 q^{3} + 39 q^{4} + 12 q^{6} - 35 q^{9} + O(q^{10}) \) \( 86 q + 3 q^{2} + 2 q^{3} + 39 q^{4} + 12 q^{6} - 35 q^{9} - 9 q^{10} - 6 q^{11} + 8 q^{12} + q^{13} - 36 q^{15} - 29 q^{16} + q^{17} + 6 q^{19} + 9 q^{20} - 12 q^{22} + 4 q^{23} - 6 q^{24} - 40 q^{25} + 39 q^{26} - 4 q^{27} - 11 q^{29} + 38 q^{30} - 27 q^{32} + 30 q^{33} + 31 q^{36} - 15 q^{37} - 16 q^{38} - 6 q^{39} - 98 q^{40} - 21 q^{41} - 16 q^{43} + 3 q^{45} - 6 q^{46} - 8 q^{48} + 78 q^{50} + 12 q^{51} - 4 q^{52} + 14 q^{53} - 24 q^{54} + 6 q^{55} - 93 q^{58} - 30 q^{59} - 13 q^{61} - 2 q^{62} + 38 q^{64} + 11 q^{65} + 52 q^{66} + 42 q^{67} + 11 q^{68} - 16 q^{69} - 24 q^{71} + 45 q^{72} - 21 q^{74} - 42 q^{75} + 24 q^{76} - 42 q^{78} + 96 q^{79} + 87 q^{80} - 23 q^{81} - 23 q^{82} + 27 q^{85} + 8 q^{87} + 38 q^{88} + 24 q^{89} - 30 q^{90} - 40 q^{92} + 60 q^{93} + 2 q^{94} + 56 q^{95} - 18 q^{97} + O(q^{100}) \)

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.q.a 637.q 13.e $2$ $5.086$ \(\Q(\sqrt{-3}) \) None 13.2.e.a \(-3\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.q.b 637.q 13.e $2$ $5.086$ \(\Q(\sqrt{-3}) \) None 91.2.k.a \(3\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.q.c 637.q 13.e $2$ $5.086$ \(\Q(\sqrt{-3}) \) None 91.2.k.a \(3\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.q.d 637.q 13.e $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{-13})\) None 637.2.q.d \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\beta _{2})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
637.2.q.e 637.q 13.e $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 637.2.q.e \(3\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{3})q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
637.2.q.f 637.q 13.e $4$ $5.086$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 637.2.q.e \(3\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{3})q^{2}+(-1+2\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
637.2.q.g 637.q 13.e $12$ $5.086$ 12.0.\(\cdots\).1 None 91.2.k.b \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{10}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.q.h 637.q 13.e $12$ $5.086$ 12.0.\(\cdots\).1 None 91.2.q.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{8}q^{2}+(-\beta _{4}-\beta _{9})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.q.i 637.q 13.e $12$ $5.086$ 12.0.\(\cdots\).1 None 91.2.k.b \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{4}-\beta _{6})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
637.2.q.j 637.q 13.e $32$ $5.086$ 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

\( S_{2}^{\mathrm{old}}(637, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)