Properties

Label 3150.2.bu
Level 3150
Weight 2
Character orbit bu
Rep. character \(\chi_{3150}(379,\cdot)\)
Character field \(\Q(\zeta_{10})\)
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.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2944 304 2640
Cusp forms 2816 304 2512
Eisenstein series 128 0 128

Trace form

\( 304q + 76q^{4} - 16q^{5} + O(q^{10}) \) \( 304q + 76q^{4} - 16q^{5} + 4q^{11} - 4q^{14} - 76q^{16} + 24q^{19} - 4q^{20} + 20q^{22} - 20q^{23} - 88q^{25} + 8q^{26} - 32q^{29} - 24q^{31} + 12q^{34} - 4q^{35} + 8q^{41} - 4q^{44} - 20q^{46} - 140q^{47} - 304q^{49} + 12q^{50} + 20q^{53} + 12q^{55} + 4q^{56} + 36q^{59} - 40q^{61} + 76q^{64} + 80q^{65} + 140q^{67} - 4q^{70} - 32q^{71} + 80q^{73} + 72q^{74} + 16q^{76} + 40q^{77} + 56q^{79} + 4q^{80} + 60q^{83} + 96q^{85} + 20q^{86} + 76q^{89} - 4q^{91} + 4q^{95} + 60q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database