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Properties

Label 2695.2.t
Level $2695$
Weight $2$
Character orbit 2695.t
Rep. character $\chi_{2695}(1684,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $400$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 704 400 304
Cusp forms 640 400 240
Eisenstein series 64 0 64

Trace form

\( 400 q + 200 q^{4} + 8 q^{6} + 204 q^{9} + O(q^{10}) \) \( 400 q + 200 q^{4} + 8 q^{6} + 204 q^{9} + 6 q^{10} + 44 q^{15} - 204 q^{16} + 8 q^{19} + 24 q^{20} + 12 q^{24} - 8 q^{25} - 16 q^{26} - 64 q^{29} + 28 q^{30} - 12 q^{31} + 24 q^{34} + 584 q^{36} + 40 q^{39} - 64 q^{40} - 8 q^{41} + 4 q^{44} - 6 q^{45} + 28 q^{46} - 88 q^{50} + 24 q^{51} + 4 q^{54} + 44 q^{59} + 68 q^{60} - 20 q^{61} - 488 q^{64} + 78 q^{65} - 16 q^{66} + 32 q^{69} - 32 q^{71} - 64 q^{74} + 12 q^{75} - 56 q^{76} + 32 q^{79} + 50 q^{80} - 336 q^{81} - 56 q^{85} - 108 q^{86} + 84 q^{89} + 188 q^{90} - 56 q^{94} + 20 q^{95} + 84 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2695, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)