Properties

Label 630.2.r
Level 630
Weight 2
Character orbit r
Rep. character \(\chi_{630}(59,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 96
Newform subspaces 2
Sturm bound 288
Trace bound 2

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(13\)

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

\( 96q - 48q^{4} + 6q^{9} + O(q^{10}) \) \( 96q - 48q^{4} + 6q^{9} + 6q^{14} + 2q^{15} - 48q^{16} + 10q^{21} + 6q^{24} - 6q^{29} + 2q^{30} + 30q^{35} + 6q^{41} - 12q^{44} + 18q^{45} + 6q^{46} - 12q^{49} - 36q^{50} - 16q^{51} - 10q^{60} - 18q^{61} + 96q^{64} - 54q^{65} - 48q^{66} + 84q^{69} + 6q^{70} - 30q^{75} - 74q^{81} - 26q^{84} + 66q^{89} + 54q^{90} + 66q^{95} - 6q^{96} - 52q^{99} + O(q^{100}) \)

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.r.a \(48\) \(5.031\) None \(-24\) \(3\) \(0\) \(0\)
630.2.r.b \(48\) \(5.031\) None \(24\) \(-3\) \(0\) \(0\)

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