↑

Properties

Label 342.10.s
Level $342$
Weight $10$
Character orbit 342.s
Rep. character $\chi_{342}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
Sturm bound $600$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 342.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(342, [\chi])\).

Total New Old
Modular forms 1096 120 976
Cusp forms 1064 120 944
Eisenstein series 32 0 32

Trace form

\( 120 q - 15360 q^{4} - 3192 q^{7} + O(q^{10}) \) \( 120 q - 15360 q^{4} - 3192 q^{7} + 421668 q^{13} - 3932160 q^{16} + 1405896 q^{19} + 2042496 q^{22} + 29682420 q^{25} + 408576 q^{28} - 639360 q^{34} - 28915788 q^{43} + 461130624 q^{49} - 107947008 q^{52} + 95445144 q^{55} + 168173568 q^{58} - 64980492 q^{61} + 2013265920 q^{64} - 1059470316 q^{67} + 1469937024 q^{70} - 1172540388 q^{73} + 165479424 q^{76} - 36275868 q^{79} - 183711744 q^{82} - 2890987992 q^{85} - 2004787764 q^{91} - 3252948120 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{10}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)