Properties

Label 3150.2.k
Level 3150
Weight 2
Character orbit k
Rep. character \(\chi_{3150}(1801,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 128
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
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 1536 128 1408
Cusp forms 1344 128 1216
Eisenstein series 192 0 192

Trace form

\( 128q - 64q^{4} + 4q^{7} + O(q^{10}) \) \( 128q - 64q^{4} + 4q^{7} - 8q^{11} + 4q^{14} - 64q^{16} + 16q^{17} - 12q^{19} - 8q^{23} - 12q^{26} - 8q^{28} + 16q^{31} - 4q^{37} + 4q^{38} + 24q^{41} - 24q^{43} - 8q^{44} - 8q^{46} + 8q^{47} + 20q^{49} + 32q^{53} - 8q^{56} + 4q^{58} - 28q^{59} - 16q^{61} - 8q^{62} + 128q^{64} + 40q^{67} + 16q^{68} - 32q^{71} - 12q^{73} + 8q^{74} + 24q^{76} - 60q^{77} + 32q^{79} + 16q^{82} - 48q^{83} + 12q^{86} - 8q^{89} - 36q^{91} + 16q^{92} + 28q^{94} + 72q^{97} + 48q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database