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Properties

Label 2352.2.cz
Level $2352$
Weight $2$
Character orbit 2352.cz
Rep. character $\chi_{2352}(95,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1344$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.cz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 588 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 5520 1344 4176
Cusp forms 5232 1344 3888
Eisenstein series 288 0 288

Trace form

\( 1344 q + O(q^{10}) \) \( 1344 q - 8 q^{13} + 12 q^{21} - 124 q^{25} - 32 q^{37} + 12 q^{45} - 8 q^{49} - 20 q^{61} - 72 q^{69} - 20 q^{73} + 96 q^{81} + 24 q^{93} + 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)