Properties

Label 630.2.bw
Level 630
Weight 2
Character orbit bw
Rep. character \(\chi_{630}(103,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 192
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.bw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{12})\)
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 608 192 416
Cusp forms 544 192 352
Eisenstein series 64 0 64

Trace form

\( 192q + O(q^{10}) \) \( 192q + 8q^{11} - 12q^{15} - 192q^{16} + 36q^{17} - 8q^{18} + 8q^{23} + 36q^{27} + 12q^{30} + 48q^{35} - 16q^{36} - 12q^{41} + 4q^{42} + 48q^{45} + 12q^{46} - 16q^{50} - 24q^{51} - 40q^{53} - 4q^{56} - 32q^{57} - 12q^{58} - 16q^{60} - 12q^{63} + 16q^{65} - 36q^{68} + 16q^{71} - 8q^{72} + 96q^{75} - 64q^{77} - 16q^{78} + 16q^{81} + 168q^{83} + 8q^{86} - 36q^{87} - 36q^{90} + 8q^{92} - 48q^{93} - 128q^{95} - 48q^{98} + O(q^{100}) \)

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.bw.a \(192\) \(5.031\) 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