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Properties

Label 546.4.bw
Level $546$
Weight $4$
Character orbit 546.bw
Rep. character $\chi_{546}(11,\cdot)$
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.bw (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

\( 448 q - 20 q^{7} + O(q^{10}) \) \( 448 q - 20 q^{7} - 168 q^{15} + 3584 q^{16} + 208 q^{18} + 848 q^{19} - 40 q^{21} - 552 q^{27} - 592 q^{28} - 716 q^{31} + 1032 q^{33} - 768 q^{36} - 812 q^{37} + 856 q^{39} - 576 q^{42} - 420 q^{43} - 160 q^{45} + 480 q^{46} - 2016 q^{49} + 160 q^{52} + 240 q^{54} - 480 q^{55} + 424 q^{57} - 96 q^{58} - 672 q^{60} - 768 q^{61} + 2540 q^{63} + 2080 q^{66} + 884 q^{67} - 3696 q^{69} + 384 q^{70} - 512 q^{72} + 1964 q^{73} - 4048 q^{76} - 1424 q^{78} - 4416 q^{79} + 1824 q^{81} + 160 q^{84} + 8448 q^{85} - 2640 q^{87} + 6796 q^{91} + 1656 q^{93} + 4992 q^{94} - 1832 q^{97} + 3352 q^{99} + O(q^{100}) \)

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

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