Properties

Label 630.2.bi
Level $630$
Weight $2$
Character orbit 630.bi
Rep. character $\chi_{630}(479,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $2$
Sturm bound $288$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(630, [\chi])\).

Total New Old
Modular forms 304 96 208
Cusp forms 272 96 176
Eisenstein series 32 0 32

Trace form

\( 96 q + 96 q^{4} + O(q^{10}) \) \( 96 q + 96 q^{4} + 12 q^{11} + 6 q^{14} + 2 q^{15} + 96 q^{16} + 16 q^{21} - 6 q^{29} - 10 q^{30} - 30 q^{35} - 36 q^{39} - 6 q^{41} + 12 q^{44} - 24 q^{45} + 6 q^{46} + 6 q^{49} - 36 q^{50} + 20 q^{51} + 6 q^{56} + 2 q^{60} + 96 q^{64} - 84 q^{69} + 6 q^{70} + 36 q^{75} + 16 q^{81} + 16 q^{84} - 66 q^{89} - 54 q^{90} - 52 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
630.2.bi.a 630.bi 315.aq $48$ $5.031$ None \(-48\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{6}]$
630.2.bi.b 630.bi 315.aq $48$ $5.031$ None \(48\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)