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Properties

Label 3675.2.ck
Level $3675$
Weight $2$
Character orbit 3675.ck
Rep. character $\chi_{3675}(299,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $3984$
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.ck (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 6864 4080 2784
Cusp forms 6576 3984 2592
Eisenstein series 288 96 192

Trace form

\( 3984 q + 380 q^{4} - 6 q^{9} + O(q^{10}) \) \( 3984 q + 380 q^{4} - 6 q^{9} + 260 q^{16} + 66 q^{19} - 28 q^{21} + 100 q^{24} - 60 q^{31} - 56 q^{34} - 116 q^{36} + 42 q^{39} - 328 q^{46} + 166 q^{49} - 26 q^{51} - 74 q^{54} + 50 q^{61} - 600 q^{64} + 180 q^{66} + 28 q^{69} - 504 q^{76} + 36 q^{79} - 266 q^{81} + 226 q^{84} - 298 q^{91} + 196 q^{94} - 570 q^{96} - 180 q^{99} + O(q^{100}) \)

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

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