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Properties

Label 2940.2.dc
Level $2940$
Weight $2$
Character orbit 2940.dc
Rep. character $\chi_{2940}(101,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $888$
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.dc (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
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 8208 888 7320
Cusp forms 7920 888 7032
Eisenstein series 288 0 288

Trace form

\( 888 q + 10 q^{7} - 16 q^{9} + O(q^{10}) \) \( 888 q + 10 q^{7} - 16 q^{9} - 6 q^{19} - 22 q^{21} + 74 q^{25} - 42 q^{27} - 30 q^{31} + 24 q^{33} - 40 q^{37} + 12 q^{39} + 36 q^{43} - 6 q^{45} - 30 q^{49} - 6 q^{51} - 20 q^{57} + 14 q^{61} + 50 q^{63} - 6 q^{67} + 56 q^{69} + 6 q^{73} + 10 q^{79} + 120 q^{81} + 242 q^{87} + 134 q^{91} + 14 q^{93} + 92 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2940, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1470, [\chi])\)\(^{\oplus 2}\)