Properties

Label 546.4.bn
Level $546$
Weight $4$
Character orbit 546.bn
Rep. character $\chi_{546}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $224$
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.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 688 224 464
Cusp forms 656 224 432
Eisenstein series 32 0 32

Trace form

\( 224 q - 448 q^{4} + 36 q^{7} - 64 q^{9} + O(q^{10}) \) \( 224 q - 448 q^{4} + 36 q^{7} - 64 q^{9} + 18 q^{13} - 120 q^{15} - 1792 q^{16} + 192 q^{18} + 504 q^{19} + 2800 q^{25} - 216 q^{28} + 440 q^{30} - 30 q^{31} + 744 q^{33} + 128 q^{36} + 168 q^{37} - 198 q^{39} + 208 q^{42} + 254 q^{43} + 360 q^{46} - 340 q^{49} + 702 q^{51} - 672 q^{52} - 180 q^{54} - 720 q^{55} + 480 q^{60} - 4344 q^{63} + 14336 q^{64} - 1200 q^{66} + 2628 q^{69} - 288 q^{70} - 54 q^{73} - 2088 q^{75} - 1008 q^{76} - 344 q^{78} + 3902 q^{79} - 1168 q^{81} + 3816 q^{85} - 312 q^{87} + 1690 q^{91} + 780 q^{93} + 3696 q^{97} + O(q^{100}) \)

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

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