↑

Properties

Label 354.6.g
Level $354$
Weight $6$
Character orbit 354.g
Rep. character $\chi_{354}(11,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $2800$
Sturm bound $360$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 354.g (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(354, [\chi])\).

Total New Old
Modular forms 8512 2800 5712
Cusp forms 8288 2800 5488
Eisenstein series 224 0 224

Trace form

\( 2800 q + 26 q^{3} - 1600 q^{4} - 76 q^{7} - 102 q^{9} + O(q^{10}) \) \( 2800 q + 26 q^{3} - 1600 q^{4} - 76 q^{7} - 102 q^{9} + 416 q^{12} + 4214 q^{15} - 25600 q^{16} + 1788 q^{19} + 7602 q^{21} - 5216 q^{22} + 47912 q^{25} - 19780 q^{27} - 1216 q^{28} - 1632 q^{36} - 516852 q^{45} + 19648 q^{46} + 6656 q^{48} - 171536 q^{49} + 572164 q^{51} - 117740 q^{54} - 764972 q^{57} - 436480 q^{60} - 151572 q^{63} - 409600 q^{64} + 778708 q^{66} + 1309640 q^{69} - 1447514 q^{75} + 28608 q^{76} + 11104 q^{78} + 137316 q^{79} - 94190 q^{81} + 121632 q^{84} + 277048 q^{85} - 276522 q^{87} - 83456 q^{88} - 217152 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(354, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)