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Properties

Label 3675.2.cc
Level $3675$
Weight $2$
Character orbit 3675.cc
Rep. character $\chi_{3675}(509,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $3136$
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.cc (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 4608 3264 1344
Cusp forms 4352 3136 1216
Eisenstein series 256 128 128

Trace form

\( 3136 q + 15 q^{3} + 390 q^{4} + 3 q^{9} + O(q^{10}) \) \( 3136 q + 15 q^{3} + 390 q^{4} + 3 q^{9} + 30 q^{10} + 15 q^{12} + 20 q^{15} + 366 q^{16} + 18 q^{19} + 30 q^{24} - 6 q^{25} + 19 q^{30} + 90 q^{33} - 140 q^{36} + 10 q^{37} + 31 q^{39} - 42 q^{40} + 117 q^{45} + 18 q^{46} + 44 q^{51} + 30 q^{52} + 21 q^{54} - 110 q^{58} + 137 q^{60} + 18 q^{61} - 616 q^{64} - 57 q^{66} + 10 q^{67} - 75 q^{72} + 150 q^{73} - 33 q^{75} - 70 q^{78} + 34 q^{79} - 85 q^{81} - 56 q^{85} + 15 q^{87} - 140 q^{88} - 30 q^{94} + 9 q^{96} - 164 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)