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Properties

Label 3675.2.cw
Level $3675$
Weight $2$
Character orbit 3675.cw
Rep. character $\chi_{3675}(104,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $13344$
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.cw (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3675 \)
Character field: \(\Q(\zeta_{70})\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 13536 13536 0
Cusp forms 13344 13344 0
Eisenstein series 192 192 0

Trace form

\( 13344 q - 35 q^{3} + 522 q^{4} - 21 q^{6} - 15 q^{9} + O(q^{10}) \) \( 13344 q - 35 q^{3} + 522 q^{4} - 21 q^{6} - 15 q^{9} - 56 q^{10} - 35 q^{12} - 70 q^{13} - 8 q^{15} + 498 q^{16} - 3 q^{21} - 50 q^{22} - 56 q^{24} - 52 q^{25} - 35 q^{27} - 130 q^{28} - 56 q^{30} - 35 q^{33} + 70 q^{34} - 61 q^{36} - 50 q^{37} - 7 q^{39} - 70 q^{40} + 161 q^{45} - 6 q^{46} - 92 q^{49} - 4 q^{51} - 70 q^{52} - 21 q^{54} - 98 q^{55} - 50 q^{58} + 34 q^{60} - 42 q^{61} - 90 q^{63} + 490 q^{64} - 21 q^{66} - 120 q^{67} - 21 q^{69} - 6 q^{70} + 75 q^{72} - 70 q^{73} + 14 q^{75} + 112 q^{76} + 5 q^{78} - 16 q^{79} - 47 q^{81} + 151 q^{84} + 72 q^{85} - 35 q^{87} - 110 q^{88} + 133 q^{90} + 40 q^{91} - 42 q^{94} - 49 q^{96} - 60 q^{99} + O(q^{100}) \)

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.