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Properties

Label 392.6.e
Level $392$
Weight $6$
Character orbit 392.e
Rep. character $\chi_{392}(195,\cdot)$
Character field $\Q$
Dimension $196$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 392.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(392, [\chi])\).

Total New Old
Modular forms 288 204 84
Cusp forms 272 196 76
Eisenstein series 16 8 8

Trace form

\( 196 q - 20 q^{4} - 72 q^{8} - 15224 q^{9} + O(q^{10}) \) \( 196 q - 20 q^{4} - 72 q^{8} - 15224 q^{9} + 1212 q^{11} + 1332 q^{16} + 4208 q^{18} + 7100 q^{22} + 112504 q^{25} - 11796 q^{30} + 12700 q^{32} + 49828 q^{36} - 32080 q^{43} - 59140 q^{44} - 26280 q^{46} - 140804 q^{50} - 14412 q^{51} + 24796 q^{57} + 147124 q^{58} + 9132 q^{60} - 97532 q^{64} + 12504 q^{65} + 150420 q^{67} + 316844 q^{72} - 89292 q^{74} + 171316 q^{78} + 1164716 q^{81} - 152824 q^{86} - 58612 q^{88} + 372908 q^{92} - 254024 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(392, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(392, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(392, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)