Properties

Label 637.2.x
Level $637$
Weight $2$
Character orbit 637.x
Rep. character $\chi_{637}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $172$
Newform subspaces $3$
Sturm bound $130$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(130\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 292 204 88
Cusp forms 228 172 56
Eisenstein series 64 32 32

Trace form

\( 172 q + 2 q^{2} + 6 q^{4} + 6 q^{5} - 12 q^{6} - 20 q^{8} - 140 q^{9} + O(q^{10}) \) \( 172 q + 2 q^{2} + 6 q^{4} + 6 q^{5} - 12 q^{6} - 20 q^{8} - 140 q^{9} + 12 q^{10} - 10 q^{11} - 8 q^{12} - 46 q^{15} + 66 q^{16} + 6 q^{17} - 36 q^{18} + 8 q^{19} + 36 q^{20} - 4 q^{22} + 6 q^{23} - 12 q^{24} - 24 q^{26} - 4 q^{29} + 38 q^{31} + 44 q^{32} - 18 q^{33} - 12 q^{34} - 138 q^{36} - 12 q^{37} - 96 q^{39} - 48 q^{40} - 18 q^{41} - 26 q^{44} - 12 q^{45} - 26 q^{46} + 42 q^{47} - 12 q^{48} - 90 q^{50} + 120 q^{51} + 28 q^{52} - 8 q^{53} + 30 q^{54} + 6 q^{55} + 16 q^{57} - 62 q^{58} + 6 q^{59} + 108 q^{60} + 36 q^{62} - 6 q^{65} - 66 q^{66} + 60 q^{67} - 30 q^{68} - 42 q^{69} + 10 q^{71} + 94 q^{72} - 14 q^{73} + 74 q^{74} + 20 q^{75} - 52 q^{76} + 22 q^{78} - 20 q^{79} - 12 q^{80} - 28 q^{81} + 108 q^{82} + 66 q^{83} + 102 q^{85} + 14 q^{86} - 42 q^{87} + 30 q^{89} + 72 q^{90} + 188 q^{92} + 118 q^{93} - 18 q^{95} - 18 q^{96} - 62 q^{97} + 48 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
637.2.x.a 637.x 91.w $28$ $5.086$ None \(-2\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{12}]$
637.2.x.b 637.x 91.w $32$ $5.086$ None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
637.2.x.c 637.x 91.w $112$ $5.086$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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