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Properties

Label 392.4.b
Level $392$
Weight $4$
Character orbit 392.b
Rep. character $\chi_{392}(197,\cdot)$
Character field $\Q$
Dimension $118$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 392.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 176 128 48
Cusp forms 160 118 42
Eisenstein series 16 10 6

Trace form

\( 118 q + 2 q^{2} + 14 q^{6} - 40 q^{8} - 970 q^{9} + O(q^{10}) \) \( 118 q + 2 q^{2} + 14 q^{6} - 40 q^{8} - 970 q^{9} - 76 q^{10} + 2 q^{12} - 4 q^{15} - 76 q^{16} - 24 q^{17} - 102 q^{18} - 148 q^{20} - 268 q^{22} + 28 q^{23} + 266 q^{24} - 2470 q^{25} + 332 q^{26} - 480 q^{30} + 80 q^{31} + 492 q^{32} + 64 q^{33} - 654 q^{34} + 112 q^{36} - 18 q^{38} - 664 q^{39} - 660 q^{40} - 136 q^{41} + 1124 q^{44} + 812 q^{46} - 672 q^{47} + 1674 q^{48} + 362 q^{50} - 572 q^{52} - 1652 q^{54} + 48 q^{55} - 60 q^{57} + 1612 q^{58} - 1500 q^{60} + 272 q^{62} - 60 q^{64} + 624 q^{65} - 428 q^{66} + 1478 q^{68} - 1856 q^{71} - 492 q^{72} - 152 q^{73} - 1544 q^{74} - 686 q^{76} - 44 q^{78} - 324 q^{79} + 940 q^{80} + 6422 q^{81} + 3402 q^{82} + 5396 q^{86} + 3664 q^{87} - 164 q^{88} - 312 q^{89} + 1116 q^{90} + 4900 q^{92} + 1488 q^{94} + 4084 q^{95} - 4886 q^{96} - 1080 q^{97} + O(q^{100}) \)

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

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