Properties

Label 3150.2.i
Level 3150
Weight 2
Character orbit i
Rep. character \(\chi_{3150}(151,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 304
Sturm bound 1440

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.i (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

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

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