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Properties

Label 2940.2.cd
Level $2940$
Weight $2$
Character orbit 2940.cd
Rep. character $\chi_{2940}(169,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
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.cd (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4104 336 3768
Cusp forms 3960 336 3624
Eisenstein series 144 0 144

Trace form

\( 336 q - 4 q^{5} + 56 q^{9} + O(q^{10}) \) \( 336 q - 4 q^{5} + 56 q^{9} - 12 q^{11} - 10 q^{15} - 48 q^{19} - 4 q^{21} - 8 q^{25} + 8 q^{29} - 24 q^{31} - 20 q^{35} - 20 q^{39} + 52 q^{41} - 10 q^{45} - 20 q^{49} + 20 q^{51} + 26 q^{55} + 32 q^{59} - 4 q^{61} + 12 q^{65} + 24 q^{69} - 8 q^{71} + 16 q^{75} - 56 q^{81} + 40 q^{85} + 8 q^{89} - 20 q^{91} + 76 q^{95} - 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)