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Properties

Label 343.4.g
Level $343$
Weight $4$
Character orbit 343.g
Rep. character $\chi_{343}(30,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $780$
Sturm bound $130$

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Defining parameters

Level: \( N \) \(=\) \( 343 = 7^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 343.g (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(130\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(343, [\chi])\).

Total New Old
Modular forms 1260 900 360
Cusp forms 1092 780 312
Eisenstein series 168 120 48

Trace form

\( 780 q + 13 q^{2} + 7 q^{3} + 253 q^{4} + 7 q^{5} + 70 q^{6} - 76 q^{8} + 396 q^{9} - 85 q^{11} + 427 q^{12} - 14 q^{13} - 290 q^{15} + 833 q^{16} - 189 q^{17} - 80 q^{18} + 490 q^{19} + 406 q^{20} - 650 q^{22}+ \cdots + 10660 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(343, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(343, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(343, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)