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Properties

Label 392.4.m
Level $392$
Weight $4$
Character orbit 392.m
Rep. character $\chi_{392}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $232$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 392.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(392, [\chi])\).

Total New Old
Modular forms 352 248 104
Cusp forms 320 232 88
Eisenstein series 32 16 16

Trace form

\( 232 q + 3 q^{2} + 6 q^{3} - 9 q^{4} + 18 q^{8} + 974 q^{9} + O(q^{10}) \) \( 232 q + 3 q^{2} + 6 q^{3} - 9 q^{4} + 18 q^{8} + 974 q^{9} + 12 q^{10} + 42 q^{11} - 162 q^{12} + 123 q^{16} + 6 q^{17} - 119 q^{18} + 6 q^{19} - 68 q^{22} + 354 q^{24} - 2498 q^{25} + 402 q^{26} - 402 q^{30} - 847 q^{32} + 6 q^{33} + 158 q^{36} - 1614 q^{38} + 798 q^{40} - 1632 q^{43} + 598 q^{44} + 1202 q^{46} + 98 q^{50} + 486 q^{51} - 2208 q^{52} - 1170 q^{54} - 244 q^{57} - 262 q^{58} + 2070 q^{59} + 2574 q^{60} - 2622 q^{64} + 252 q^{65} + 3138 q^{66} + 1118 q^{67} - 3048 q^{68} + 499 q^{72} - 642 q^{73} - 1638 q^{74} - 744 q^{75} + 4028 q^{78} + 3276 q^{80} - 7472 q^{81} + 2430 q^{82} + 1420 q^{86} + 4618 q^{88} + 1278 q^{89} + 1240 q^{92} + 246 q^{94} + 5652 q^{96} + 776 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(392, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(392, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(392, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)