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Properties

Label 2940.2.cz
Level $2940$
Weight $2$
Character orbit 2940.cz
Rep. character $\chi_{2940}(271,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2688$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2940.cz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2940, [\chi])\).

Total New Old
Modular forms 8160 2688 5472
Cusp forms 7968 2688 5280
Eisenstein series 192 0 192

Trace form

\( 2688 q + 224 q^{9} + O(q^{10}) \) \( 2688 q + 224 q^{9} - 16 q^{14} - 8 q^{16} - 16 q^{21} - 24 q^{22} - 48 q^{24} - 224 q^{25} + 60 q^{26} - 92 q^{28} + 20 q^{32} - 56 q^{34} - 64 q^{37} + 12 q^{42} + 64 q^{44} + 20 q^{46} - 8 q^{49} - 36 q^{52} + 16 q^{53} + 60 q^{56} + 48 q^{57} + 28 q^{58} - 8 q^{61} + 8 q^{65} - 36 q^{66} + 60 q^{68} + 4 q^{70} - 72 q^{73} - 16 q^{77} + 24 q^{78} + 224 q^{81} + 292 q^{82} - 36 q^{84} + 384 q^{86} - 4 q^{88} + 16 q^{92} + 8 q^{93} + 636 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2940, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2940, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)