Properties

Label 630.2.ca
Level 630
Weight 2
Character orbit ca
Rep. character \(\chi_{630}(113,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 144
Newform subspaces 2
Sturm bound 288
Trace bound 14

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.ca (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(13\)

Dimensions

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

Total New Old
Modular forms 608 144 464
Cusp forms 544 144 400
Eisenstein series 64 0 64

Trace form

\( 144q - 8q^{3} + O(q^{10}) \) \( 144q - 8q^{3} + 24q^{11} + 8q^{12} - 8q^{15} + 72q^{16} + 8q^{18} + 24q^{20} + 8q^{21} + 24q^{23} + 24q^{25} + 16q^{27} + 8q^{33} - 8q^{36} + 48q^{37} - 72q^{38} - 96q^{41} - 80q^{45} - 96q^{47} - 16q^{48} + 32q^{51} + 48q^{55} - 32q^{57} - 8q^{63} + 24q^{65} + 16q^{66} + 24q^{67} + 16q^{72} - 32q^{75} + 32q^{78} + 96q^{82} - 120q^{83} + 48q^{85} + 144q^{86} - 40q^{87} - 40q^{90} - 48q^{91} + 24q^{92} - 32q^{93} - 120q^{95} + 72q^{97} + O(q^{100}) \)

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.ca.a \(72\) \(5.031\) None \(0\) \(-4\) \(0\) \(0\)
630.2.ca.b \(72\) \(5.031\) None \(0\) \(-4\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database