Properties

Label 3150.2.j
Level 3150
Weight 2
Character orbit j
Rep. character \(\chi_{3150}(1051,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 228
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
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 228 1260
Cusp forms 1392 228 1164
Eisenstein series 96 0 96

Trace form

\( 228q + 2q^{2} - 2q^{3} - 114q^{4} + 2q^{6} - 4q^{8} + 6q^{9} + O(q^{10}) \) \( 228q + 2q^{2} - 2q^{3} - 114q^{4} + 2q^{6} - 4q^{8} + 6q^{9} - 2q^{11} - 8q^{12} - 4q^{14} - 114q^{16} + 4q^{17} - 8q^{18} + 12q^{19} - 4q^{21} - 6q^{22} - 4q^{23} + 2q^{24} - 20q^{27} - 32q^{29} + 12q^{31} + 2q^{32} + 6q^{33} - 6q^{34} + 6q^{36} - 24q^{37} + 10q^{38} - 4q^{39} + 14q^{41} - 6q^{43} + 4q^{44} + 48q^{47} + 10q^{48} - 114q^{49} - 38q^{51} - 16q^{53} + 62q^{54} - 4q^{56} - 54q^{57} - 54q^{59} + 24q^{62} + 4q^{63} + 228q^{64} + 12q^{66} + 6q^{67} - 2q^{68} + 96q^{69} + 80q^{71} + 10q^{72} + 12q^{73} - 4q^{74} - 6q^{76} + 8q^{77} - 28q^{78} + 12q^{79} + 78q^{81} + 60q^{82} - 4q^{83} + 8q^{84} - 54q^{86} + 56q^{87} - 6q^{88} - 184q^{89} - 24q^{91} - 4q^{92} - 56q^{93} - 4q^{96} - 18q^{97} - 4q^{98} + 112q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database