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Properties

Label 2352.4.dn
Level $2352$
Weight $4$
Character orbit 2352.dn
Rep. character $\chi_{2352}(115,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $16128$
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.dn (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1792\)

Dimensions

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

Total New Old
Modular forms 32352 16128 16224
Cusp forms 32160 16128 16032
Eisenstein series 192 0 192

Trace form

\( 16128 q - 168 q^{8} + O(q^{10}) \) \( 16128 q - 168 q^{8} + 36 q^{10} - 416 q^{14} + 504 q^{22} - 164 q^{28} + 1008 q^{34} - 456 q^{35} + 1332 q^{40} - 660 q^{42} + 9856 q^{44} + 700 q^{46} - 2856 q^{50} - 2160 q^{52} - 3080 q^{56} - 364 q^{58} - 4128 q^{59} + 6888 q^{64} - 4104 q^{66} - 1848 q^{67} + 6060 q^{68} + 6220 q^{70} - 2240 q^{71} - 2156 q^{74} + 4284 q^{76} - 3528 q^{78} - 45144 q^{80} - 108864 q^{81} - 6960 q^{82} + 1800 q^{84} - 5628 q^{86} + 4004 q^{88} - 9104 q^{91} + 9296 q^{92} - 14580 q^{94} - 7740 q^{96} + 16576 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)