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Properties

Label 546.4.bd
Level $546$
Weight $4$
Character orbit 546.bd
Rep. character $\chi_{546}(121,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
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.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 688 112 576
Cusp forms 656 112 544
Eisenstein series 32 0 32

Trace form

\( 112 q + 224 q^{4} + 36 q^{7} + 1008 q^{9} + O(q^{10}) \) \( 112 q + 224 q^{4} + 36 q^{7} + 1008 q^{9} + 160 q^{10} - 70 q^{13} - 32 q^{14} - 896 q^{16} - 4 q^{17} + 168 q^{21} - 56 q^{22} + 176 q^{23} + 1528 q^{25} + 152 q^{26} + 216 q^{28} - 172 q^{29} + 210 q^{31} + 112 q^{35} + 2016 q^{36} - 840 q^{37} + 248 q^{38} + 42 q^{39} + 320 q^{40} + 576 q^{41} - 446 q^{43} - 336 q^{44} + 360 q^{46} + 144 q^{47} + 856 q^{49} - 2208 q^{50} - 276 q^{51} + 112 q^{52} + 148 q^{53} + 552 q^{55} - 352 q^{56} - 5200 q^{61} - 1768 q^{62} + 324 q^{63} - 7168 q^{64} - 1484 q^{65} + 1056 q^{66} + 16 q^{68} - 1008 q^{69} + 2880 q^{70} + 2520 q^{71} + 2346 q^{73} + 312 q^{74} + 312 q^{75} + 1344 q^{76} - 5536 q^{77} - 864 q^{78} - 694 q^{79} + 9072 q^{81} + 2912 q^{82} + 552 q^{84} - 696 q^{85} + 504 q^{86} - 936 q^{87} - 448 q^{88} + 6792 q^{89} + 1440 q^{90} + 4502 q^{91} + 1408 q^{92} + 2646 q^{93} - 3456 q^{94} - 168 q^{95} + 2688 q^{97} + 816 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)