Properties

Label 3150.2.bl
Level 3150
Weight 2
Character orbit bl
Rep. character \(\chi_{3150}(101,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 304
Sturm bound 1440

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Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 1488 304 1184
Cusp forms 1392 304 1088
Eisenstein series 96 0 96

Trace form

\( 304q - 304q^{4} + 2q^{7} + O(q^{10}) \) \( 304q - 304q^{4} + 2q^{7} - 12q^{11} + 6q^{13} + 6q^{14} + 304q^{16} + 18q^{17} - 4q^{18} - 8q^{21} - 30q^{23} + 12q^{26} - 2q^{28} - 6q^{29} - 2q^{37} + 24q^{39} + 6q^{41} - 28q^{42} - 2q^{43} + 12q^{44} - 6q^{46} - 36q^{47} + 4q^{49} + 38q^{51} - 6q^{52} - 36q^{53} + 18q^{54} - 6q^{56} + 6q^{57} - 6q^{58} + 60q^{59} - 36q^{62} - 64q^{63} - 304q^{64} + 24q^{66} - 28q^{67} - 18q^{68} + 42q^{69} + 4q^{72} + 18q^{74} + 54q^{77} - 16q^{78} - 40q^{79} + 4q^{81} + 8q^{84} + 24q^{86} + 12q^{87} + 24q^{89} - 12q^{91} + 30q^{92} + 70q^{93} + 6q^{97} - 24q^{98} + 10q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database