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Properties

Label 3675.2.cq
Level $3675$
Weight $2$
Character orbit 3675.cq
Rep. character $\chi_{3675}(178,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3200$
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.cq (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 9216 3200 6016
Cusp forms 8704 3200 5504
Eisenstein series 512 0 512

Trace form

\( 3200 q - 12 q^{5} - 24 q^{8} + O(q^{10}) \) \( 3200 q - 12 q^{5} - 24 q^{8} - 12 q^{10} - 8 q^{15} - 400 q^{16} + 136 q^{22} - 80 q^{23} + 20 q^{25} + 160 q^{29} - 64 q^{30} + 24 q^{32} - 36 q^{33} + 800 q^{36} - 4 q^{37} + 192 q^{38} + 12 q^{40} - 104 q^{43} - 60 q^{47} - 288 q^{50} + 432 q^{52} - 176 q^{53} + 32 q^{57} + 108 q^{58} + 240 q^{59} + 20 q^{60} - 120 q^{64} - 20 q^{65} + 24 q^{67} + 132 q^{68} + 12 q^{72} + 36 q^{73} + 48 q^{75} + 128 q^{78} - 12 q^{80} - 400 q^{81} + 252 q^{82} - 88 q^{85} - 24 q^{87} - 272 q^{88} - 120 q^{92} + 192 q^{93} - 316 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)