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Properties

Label 354.4.g
Level $354$
Weight $4$
Character orbit 354.g
Rep. character $\chi_{354}(11,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $1680$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 354.g (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(354, [\chi])\).

Total New Old
Modular forms 5152 1680 3472
Cusp forms 4928 1680 3248
Eisenstein series 224 0 224

Trace form

\( 1680 q - 10 q^{3} - 240 q^{4} - 12 q^{7} - 54 q^{9} + O(q^{10}) \) \( 1680 q - 10 q^{3} - 240 q^{4} - 12 q^{7} - 54 q^{9} - 40 q^{12} - 40 q^{15} - 960 q^{16} - 180 q^{19} - 264 q^{21} - 240 q^{22} + 2160 q^{25} + 110 q^{27} - 48 q^{28} - 216 q^{36} - 5436 q^{45} + 96 q^{46} - 160 q^{48} - 4032 q^{49} - 836 q^{51} + 7714 q^{54} + 14548 q^{57} + 9584 q^{60} + 9246 q^{63} - 3840 q^{64} + 1750 q^{66} - 12064 q^{69} - 10508 q^{75} - 720 q^{76} + 2608 q^{78} - 1476 q^{79} + 2434 q^{81} - 1056 q^{84} - 2352 q^{85} - 1068 q^{87} - 960 q^{88} + 3168 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(354, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(354, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(354, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(177, [\chi])\)\(^{\oplus 2}\)