Properties

Label 630.2.bq
Level 630
Weight 2
Character orbit bq
Rep. character \(\chi_{630}(79,\cdot)\)
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.bq (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

\( 96q + 48q^{4} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 96q + 48q^{4} - 4q^{6} + 2q^{9} - 8q^{11} - 2q^{14} - 2q^{15} - 48q^{16} + 14q^{21} - 2q^{24} + 24q^{26} + 10q^{29} - 2q^{30} - 34q^{35} - 8q^{36} + 8q^{39} + 30q^{41} - 4q^{44} + 10q^{45} - 6q^{46} + 12q^{49} - 12q^{50} - 8q^{51} + 4q^{54} + 12q^{55} - 4q^{56} - 24q^{59} - 10q^{60} - 6q^{61} - 96q^{64} + 18q^{65} - 16q^{66} + 36q^{69} + 6q^{70} - 32q^{71} - 14q^{75} + 70q^{81} + 22q^{84} - 8q^{86} - 66q^{89} - 22q^{90} - 12q^{94} + 30q^{95} + 2q^{96} - 4q^{99} + O(q^{100}) \)

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.bq.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