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Properties

Label 2352.4.u
Level $2352$
Weight $4$
Character orbit 2352.u
Rep. character $\chi_{2352}(979,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $960$
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 960 1760
Cusp forms 2656 960 1696
Eisenstein series 64 0 64

Trace form

\( 960 q + 40 q^{4} + 168 q^{8} + O(q^{10}) \) \( 960 q + 40 q^{4} + 168 q^{8} - 80 q^{11} + 120 q^{16} - 72 q^{18} - 32 q^{22} + 1312 q^{23} + 800 q^{29} + 32 q^{37} + 1616 q^{43} + 3464 q^{44} + 1400 q^{46} + 1456 q^{50} - 1504 q^{53} + 160 q^{58} + 2448 q^{60} - 5936 q^{64} - 2880 q^{67} - 896 q^{71} - 1224 q^{72} - 6944 q^{74} + 3384 q^{78} - 77760 q^{81} - 15336 q^{86} - 2224 q^{88} - 14664 q^{92} + 720 q^{99} + O(q^{100}) \)

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

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