↑

Properties

Label 546.4.cg
Level $546$
Weight $4$
Character orbit 546.cg
Rep. character $\chi_{546}(145,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $224$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 546.cg (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

\( 224 q - 8 q^{7} + 1008 q^{9} + O(q^{10}) \) \( 224 q - 8 q^{7} + 1008 q^{9} - 112 q^{11} - 96 q^{12} - 80 q^{14} - 3584 q^{16} + 588 q^{19} - 12 q^{21} - 112 q^{22} + 112 q^{28} - 216 q^{29} + 360 q^{31} + 520 q^{35} - 728 q^{37} - 588 q^{39} - 264 q^{41} - 924 q^{43} + 224 q^{44} - 1808 q^{46} + 180 q^{49} + 1472 q^{50} - 360 q^{51} + 144 q^{52} - 1480 q^{53} - 3312 q^{55} + 192 q^{56} + 168 q^{57} - 752 q^{58} - 600 q^{61} - 4176 q^{62} - 468 q^{63} - 4120 q^{65} + 468 q^{67} + 288 q^{70} - 208 q^{71} - 3600 q^{73} - 4576 q^{74} - 8400 q^{75} + 1296 q^{76} - 1056 q^{78} + 1664 q^{79} - 9072 q^{81} + 864 q^{82} - 3792 q^{83} + 1296 q^{84} + 672 q^{85} + 784 q^{86} + 8448 q^{89} + 1512 q^{91} + 2816 q^{92} - 3780 q^{93} + 7392 q^{94} + 360 q^{97} + 6336 q^{98} - 504 q^{99} + O(q^{100}) \)

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

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