Properties

Label 637.2.i
Level $637$
Weight $2$
Character orbit 637.i
Rep. character $\chi_{637}(489,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $2$
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.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
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 144 104 40
Cusp forms 112 88 24
Eisenstein series 32 16 16

Trace form

\( 88 q + 4 q^{2} - 16 q^{8} - 72 q^{9} + O(q^{10}) \) \( 88 q + 4 q^{2} - 16 q^{8} - 72 q^{9} + 4 q^{11} + 4 q^{15} - 80 q^{16} - 24 q^{18} - 8 q^{22} - 32 q^{29} - 8 q^{32} + 16 q^{37} - 20 q^{39} + 20 q^{44} + 8 q^{46} + 48 q^{50} + 8 q^{53} - 56 q^{57} + 20 q^{58} - 96 q^{60} + 48 q^{65} - 32 q^{67} - 4 q^{71} + 164 q^{72} + 184 q^{74} - 16 q^{78} - 16 q^{79} + 120 q^{81} - 60 q^{85} - 20 q^{86} - 80 q^{92} + 52 q^{93} - 24 q^{99} + O(q^{100}) \)

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.i.a 637.i 91.i $32$ $5.086$ None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
637.2.i.b 637.i 91.i $56$ $5.086$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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