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Properties

Label 343.4.e
Level $343$
Weight $4$
Character orbit 343.e
Rep. character $\chi_{343}(50,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $390$
Sturm bound $130$

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Defining parameters

Level: \( N \) \(=\) \( 343 = 7^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 343.e (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(130\)

Dimensions

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

Total New Old
Modular forms 630 450 180
Cusp forms 546 390 156
Eisenstein series 84 60 24

Trace form

\( 390 q + 5 q^{2} + 5 q^{3} - 235 q^{4} + 23 q^{5} - 19 q^{6} + q^{8} - 420 q^{9} - 9 q^{10} + 103 q^{11} - 364 q^{12} + 35 q^{13} + 215 q^{15} - 755 q^{16} + 285 q^{17} + 80 q^{18} - 628 q^{19} - 553 q^{20}+ \cdots - 10840 q^{99}+O(q^{100}) \) 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

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