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Properties

Label 2695.2.cp
Level $2695$
Weight $2$
Character orbit 2695.cp
Rep. character $\chi_{2695}(313,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3712$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2695.cp (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2695, [\chi])\).

Total New Old
Modular forms 5632 3968 1664
Cusp forms 5120 3712 1408
Eisenstein series 512 256 256

Trace form

\( 3712 q + 6 q^{2} + 18 q^{3} + 30 q^{5} - 64 q^{8} + O(q^{10}) \) \( 3712 q + 6 q^{2} + 18 q^{3} + 30 q^{5} - 64 q^{8} + 72 q^{10} + 28 q^{11} + 72 q^{12} - 72 q^{15} - 396 q^{16} + 18 q^{17} + 50 q^{18} - 32 q^{22} + 32 q^{23} + 50 q^{25} + 12 q^{26} - 6 q^{30} + 36 q^{31} + 180 q^{33} + 480 q^{36} + 26 q^{37} + 18 q^{38} + 18 q^{40} - 88 q^{43} + 144 q^{45} - 140 q^{46} + 6 q^{47} + 16 q^{50} + 100 q^{51} - 30 q^{52} + 26 q^{53} + 8 q^{57} - 82 q^{58} - 14 q^{60} + 36 q^{61} - 24 q^{65} + 48 q^{66} + 48 q^{67} - 78 q^{68} + 64 q^{71} + 10 q^{72} + 78 q^{73} - 174 q^{75} + 24 q^{78} - 210 q^{80} - 252 q^{81} + 90 q^{82} - 128 q^{85} + 100 q^{86} + 60 q^{87} + 74 q^{88} - 64 q^{92} - 154 q^{93} - 80 q^{95} - 72 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2695, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2695, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2695, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)