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Properties

Label 2352.4.dg
Level $2352$
Weight $4$
Character orbit 2352.dg
Rep. character $\chi_{2352}(17,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $4008$
Sturm bound $1792$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.dg (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2352, [\chi])\).

Total New Old
Modular forms 16272 4056 12216
Cusp forms 15984 4008 11976
Eisenstein series 288 48 240

Trace form

\( 4008 q + 11 q^{3} + 42 q^{7} - 13 q^{9} + O(q^{10}) \) \( 4008 q + 11 q^{3} + 42 q^{7} - 13 q^{9} - 28 q^{13} + 64 q^{15} - 234 q^{19} + 83 q^{21} + 8040 q^{25} + 14 q^{27} + 666 q^{31} - 11 q^{33} - 26 q^{37} + 40 q^{39} + 608 q^{43} + 649 q^{45} + 360 q^{49} - 283 q^{51} + 28 q^{55} - 145 q^{57} - 22 q^{61} + 1221 q^{63} + 390 q^{67} + 3626 q^{69} + 302 q^{73} + 1178 q^{75} - 870 q^{79} - 2477 q^{81} - 520 q^{85} - 3742 q^{87} - 2450 q^{91} - 204 q^{93} - 174 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2352, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)