Properties

Label 630.2.ba
Level 630
Weight 2
Character orbit ba
Rep. character \(\chi_{630}(499,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 96
Newform subspaces 1
Sturm bound 288
Trace bound 0

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

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

\( 96q - 96q^{4} - 4q^{6} + 8q^{9} + O(q^{10}) \) \( 96q - 96q^{4} - 4q^{6} + 8q^{9} + 4q^{11} - 2q^{14} - 2q^{15} + 96q^{16} + 8q^{21} + 4q^{24} + 24q^{26} + 10q^{29} + 10q^{30} - 34q^{35} - 8q^{36} + 44q^{39} + 30q^{41} - 4q^{44} - 44q^{45} - 6q^{46} - 6q^{49} - 12q^{50} + 28q^{51} - 8q^{54} + 12q^{55} + 2q^{56} + 48q^{59} + 2q^{60} + 12q^{61} - 96q^{64} - 36q^{65} + 32q^{66} + 36q^{69} + 6q^{70} - 32q^{71} - 68q^{75} - 32q^{81} - 8q^{84} + 4q^{86} - 66q^{89} - 22q^{90} + 24q^{94} - 60q^{95} - 4q^{96} - 4q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
630.2.ba.a \(96\) \(5.031\) None \(0\) \(0\) \(0\) \(0\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database