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Properties

Label 546.4.bx
Level $546$
Weight $4$
Character orbit 546.bx
Rep. character $\chi_{546}(97,\cdot)$
Character field $\Q(\zeta_{12})$
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.bx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 224 1152
Cusp forms 1312 224 1088
Eisenstein series 64 0 64

Trace form

\( 224 q - 44 q^{7} + 1008 q^{9} + O(q^{10}) \) \( 224 q - 44 q^{7} + 1008 q^{9} - 112 q^{11} + 160 q^{14} + 1792 q^{16} - 252 q^{21} + 224 q^{22} - 176 q^{28} + 624 q^{29} + 520 q^{35} - 3080 q^{37} + 336 q^{39} - 1176 q^{43} - 448 q^{44} - 1808 q^{46} - 2196 q^{49} + 1472 q^{50} + 608 q^{53} + 192 q^{56} + 1008 q^{57} + 1360 q^{58} + 72 q^{63} + 1184 q^{65} - 2112 q^{67} + 288 q^{70} + 4832 q^{71} - 2080 q^{74} - 1056 q^{78} - 7360 q^{79} - 9072 q^{81} + 1296 q^{84} + 4704 q^{85} + 5152 q^{86} + 7716 q^{91} + 2816 q^{92} + 8904 q^{93} + 13440 q^{95} - 1536 q^{98} + 1008 q^{99} + O(q^{100}) \)

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

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