Properties

Label 630.2.bl
Level 630
Weight 2
Character orbit bl
Rep. character \(\chi_{630}(41,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 64
Newform subspaces 2
Sturm bound 288
Trace bound 3

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Defining parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(3\)
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 64 240
Cusp forms 272 64 208
Eisenstein series 32 0 32

Trace form

\( 64q + 32q^{4} - 4q^{7} - 12q^{9} + O(q^{10}) \) \( 64q + 32q^{4} - 4q^{7} - 12q^{9} + 12q^{11} + 6q^{14} + 4q^{15} - 32q^{16} + 16q^{18} - 8q^{21} + 72q^{23} - 32q^{25} - 8q^{28} + 12q^{29} + 4q^{30} - 12q^{36} + 16q^{37} + 12q^{39} + 4q^{42} - 8q^{43} - 24q^{46} + 10q^{49} - 40q^{51} + 6q^{56} - 72q^{57} - 4q^{60} + 16q^{63} - 64q^{64} + 12q^{65} + 56q^{67} - 6q^{70} - 16q^{72} - 72q^{74} - 12q^{77} + 64q^{78} + 20q^{79} - 20q^{81} - 22q^{84} + 12q^{85} + 48q^{86} - 48q^{91} + 72q^{92} + 8q^{93} + 36q^{99} + O(q^{100}) \)

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.bl.a \(32\) \(5.031\) None \(0\) \(-4\) \(-16\) \(-2\)
630.2.bl.b \(32\) \(5.031\) None \(0\) \(4\) \(16\) \(-2\)

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

\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database