Properties

Label 630.2.cd
Level 630
Weight 2
Character orbit cd
Rep. character \(\chi_{630}(23,\cdot)\)
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.cd (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

\( 192q + 8q^{6} + O(q^{10}) \) \( 192q + 8q^{6} + 24q^{11} + 12q^{15} - 192q^{16} - 36q^{17} - 8q^{18} + 24q^{23} + 36q^{27} - 12q^{30} + 40q^{33} + 12q^{41} - 4q^{42} + 8q^{45} - 12q^{46} - 48q^{50} + 24q^{51} - 12q^{56} - 48q^{57} - 12q^{58} - 16q^{60} - 24q^{61} - 52q^{63} - 36q^{68} + 8q^{72} + 8q^{75} + 96q^{77} - 16q^{78} + 16q^{81} + 76q^{87} - 20q^{90} - 24q^{92} - 8q^{96} + O(q^{100}) \)

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.cd.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