Properties

Label 3150.2.l
Level 3150
Weight 2
Character orbit l
Rep. character \(\chi_{3150}(1201,\cdot)\)
Character field \(\Q(\zeta_{3})\)
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 304q - 152q^{4} + 4q^{6} - 2q^{7} + 2q^{9} + O(q^{10}) \) \( 304q - 152q^{4} + 4q^{6} - 2q^{7} + 2q^{9} + 8q^{11} + 2q^{13} - 2q^{14} - 152q^{16} - 2q^{17} - 4q^{18} - 4q^{19} - 6q^{21} + 20q^{23} - 2q^{24} + 8q^{26} + 12q^{27} - 2q^{28} + 10q^{29} + 2q^{31} - 18q^{33} + 8q^{36} + 2q^{37} + 24q^{38} - 22q^{39} + 30q^{41} + 22q^{42} + 2q^{43} - 4q^{44} + 6q^{46} - 6q^{47} + 10q^{49} - 12q^{51} - 4q^{52} - 16q^{53} + 10q^{54} + 4q^{56} + 34q^{57} + 12q^{58} + 2q^{59} + 20q^{61} + 20q^{62} - 42q^{63} + 304q^{64} - 8q^{66} + 14q^{67} + 4q^{68} + 26q^{69} + 44q^{71} + 8q^{72} - 28q^{73} + 12q^{74} - 4q^{76} + 14q^{77} + 16q^{78} - 16q^{79} + 50q^{81} - 40q^{83} - 6q^{84} - 8q^{86} + 32q^{87} + 36q^{89} - 16q^{91} - 10q^{92} - 70q^{93} - 12q^{94} - 2q^{96} + 2q^{97} + 24q^{98} + 26q^{99} + O(q^{100}) \)

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