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Properties

Label 2352.4.s
Level $2352$
Weight $4$
Character orbit 2352.s
Rep. character $\chi_{2352}(491,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1948$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(1792\)

Dimensions

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

Total New Old
Modular forms 2720 1988 732
Cusp forms 2656 1948 708
Eisenstein series 64 40 24

Trace form

\( 1948 q + 2 q^{3} + 4 q^{4} + 32 q^{6} + O(q^{10}) \) \( 1948 q + 2 q^{3} + 4 q^{4} + 32 q^{6} + 64 q^{10} - 76 q^{12} + 4 q^{13} + 376 q^{16} - 148 q^{18} + 28 q^{19} + 448 q^{22} - 616 q^{24} - 130 q^{27} + 864 q^{30} + 4 q^{33} + 176 q^{34} - 428 q^{36} + 4 q^{37} + 604 q^{39} - 632 q^{40} - 452 q^{43} + 252 q^{45} + 800 q^{46} + 1244 q^{48} + 972 q^{51} - 1328 q^{52} - 1592 q^{54} + 296 q^{55} - 1952 q^{58} - 3852 q^{60} - 908 q^{61} + 952 q^{64} + 1504 q^{66} + 1636 q^{67} - 52 q^{69} + 2324 q^{72} + 1850 q^{75} + 4336 q^{76} + 880 q^{78} + 4 q^{81} + 4320 q^{82} - 280 q^{85} + 1292 q^{87} + 2440 q^{88} - 4920 q^{90} - 1864 q^{93} - 1152 q^{94} - 1832 q^{96} + 8 q^{97} + 4104 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)