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Properties

Label 546.4.bv
Level $546$
Weight $4$
Character orbit 546.bv
Rep. character $\chi_{546}(317,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $448$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 546.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(546, [\chi])\).

Total New Old
Modular forms 1376 448 928
Cusp forms 1312 448 864
Eisenstein series 64 0 64

Trace form

\( 448 q + 148 q^{7} + O(q^{10}) \) \( 448 q + 148 q^{7} + 336 q^{15} + 3584 q^{16} - 128 q^{18} + 668 q^{19} - 40 q^{21} - 552 q^{27} + 224 q^{28} - 356 q^{31} - 888 q^{33} + 1540 q^{37} + 304 q^{39} + 1152 q^{42} - 160 q^{45} - 240 q^{46} + 16 q^{52} - 120 q^{54} + 960 q^{55} - 848 q^{57} + 48 q^{58} - 672 q^{60} + 384 q^{61} + 6020 q^{63} - 4160 q^{66} + 884 q^{67} - 192 q^{70} - 512 q^{72} - 2836 q^{73} - 5344 q^{76} + 2848 q^{78} + 6816 q^{79} + 7200 q^{81} - 320 q^{84} + 2400 q^{85} - 2016 q^{87} + 6364 q^{91} + 264 q^{93} + 4992 q^{94} + 2704 q^{97} - 6704 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)