Properties

Label 3150.2.u
Level 3150
Weight 2
Character orbit u
Rep. character \(\chi_{3150}(551,\cdot)\)
Character field \(\Q(\zeta_{6})\)
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 304q + 152q^{4} + 2q^{7} + 6q^{9} + O(q^{10}) \) \( 304q + 152q^{4} + 2q^{7} + 6q^{9} - 6q^{13} + 6q^{14} - 152q^{16} - 18q^{17} - 4q^{18} - 2q^{21} + 6q^{24} - 12q^{26} - 2q^{28} - 6q^{29} + 6q^{31} - 42q^{33} - 2q^{37} + 6q^{39} - 6q^{41} + 2q^{42} - 2q^{43} - 12q^{44} - 6q^{46} - 18q^{47} - 14q^{49} - 4q^{51} + 36q^{53} + 18q^{54} + 6q^{57} + 12q^{58} + 30q^{59} - 24q^{61} + 36q^{62} + 38q^{63} - 304q^{64} + 14q^{67} - 36q^{68} - 42q^{69} - 8q^{72} + 30q^{77} - 16q^{78} + 20q^{79} - 14q^{81} + 2q^{84} - 48q^{87} - 24q^{89} - 12q^{91} + 30q^{92} - 38q^{93} + 6q^{96} - 6q^{97} + 24q^{98} + 10q^{99} + O(q^{100}) \)

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