Properties

Label 3150.2.q
Level 3150
Weight 2
Character orbit q
Rep. character \(\chi_{3150}(631,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 296
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.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2944 296 2648
Cusp forms 2816 296 2520
Eisenstein series 128 0 128

Trace form

\( 296q + 2q^{2} - 74q^{4} + 18q^{5} + 2q^{8} + O(q^{10}) \) \( 296q + 2q^{2} - 74q^{4} + 18q^{5} + 2q^{8} + 2q^{10} - 4q^{11} - 12q^{13} - 4q^{14} - 74q^{16} + 4q^{17} + 24q^{19} - 12q^{20} + 12q^{22} - 28q^{23} - 14q^{25} + 12q^{26} - 12q^{29} + 24q^{31} - 8q^{32} - 18q^{34} + 4q^{35} + 10q^{37} - 24q^{38} + 2q^{40} + 12q^{41} - 8q^{43} - 4q^{44} + 20q^{46} + 28q^{47} + 296q^{49} + 6q^{50} - 12q^{52} - 2q^{53} - 100q^{55} - 4q^{56} + 4q^{58} + 36q^{59} + 60q^{61} + 16q^{62} - 74q^{64} + 82q^{65} + 12q^{67} + 4q^{68} - 4q^{70} - 48q^{71} + 76q^{73} + 92q^{74} - 16q^{76} - 24q^{77} + 56q^{79} - 2q^{80} + 44q^{82} - 52q^{83} + 58q^{85} - 20q^{86} - 8q^{88} - 34q^{89} + 4q^{91} + 32q^{92} - 20q^{95} - 16q^{97} + 2q^{98} + O(q^{100}) \)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database