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Properties

Label 3675.2.bl
Level $3675$
Weight $2$
Character orbit 3675.bl
Rep. character $\chi_{3675}(274,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1008$
Sturm bound $1120$

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Defining parameters

Level: \( N \) \(=\) \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3675.bl (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3675, [\chi])\).

Total New Old
Modular forms 3432 1008 2424
Cusp forms 3288 1008 2280
Eisenstein series 144 0 144

Trace form

\( 1008 q + 168 q^{4} - 4 q^{6} + 168 q^{9} + O(q^{10}) \) \( 1008 q + 168 q^{4} - 4 q^{6} + 168 q^{9} + 36 q^{11} - 12 q^{14} - 136 q^{16} - 108 q^{19} - 2 q^{21} + 12 q^{24} - 8 q^{26} - 16 q^{29} + 148 q^{31} + 16 q^{34} - 168 q^{36} - 10 q^{39} - 16 q^{41} + 232 q^{44} - 24 q^{46} + 34 q^{49} - 40 q^{51} + 4 q^{54} - 156 q^{56} + 48 q^{59} - 6 q^{61} + 304 q^{64} + 32 q^{66} - 144 q^{71} + 128 q^{74} + 100 q^{76} + 8 q^{79} - 168 q^{81} + 152 q^{86} - 80 q^{89} - 34 q^{91} + 56 q^{94} - 68 q^{96} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3675, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)