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Properties

Label 546.4.ch
Level $546$
Weight $4$
Character orbit 546.ch
Rep. character $\chi_{546}(137,\cdot)$
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.ch (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

\( 448 q - 56 q^{7} + O(q^{10}) \) \( 448 q - 56 q^{7} - 168 q^{15} - 7168 q^{16} - 80 q^{18} + 164 q^{19} - 40 q^{21} - 552 q^{27} + 80 q^{28} - 816 q^{30} + 64 q^{31} - 888 q^{33} - 768 q^{36} + 1288 q^{37} - 1160 q^{39} + 360 q^{42} - 420 q^{43} - 160 q^{45} - 240 q^{46} - 180 q^{49} - 1328 q^{52} - 120 q^{54} - 480 q^{55} + 424 q^{57} + 48 q^{58} + 288 q^{60} + 384 q^{61} + 1856 q^{63} + 2080 q^{66} - 3316 q^{67} - 3696 q^{69} - 192 q^{70} + 832 q^{72} - 2728 q^{73} - 4048 q^{76} - 1424 q^{78} - 4416 q^{79} - 912 q^{81} + 864 q^{82} + 160 q^{84} + 8448 q^{85} + 5280 q^{87} - 3800 q^{91} - 2088 q^{93} - 2496 q^{94} - 1832 q^{97} + 3352 q^{99} + O(q^{100}) \)

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

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