Properties

Label 3675.2.t
Level $3675$
Weight $2$
Character orbit 3675.t
Rep. character $\chi_{3675}(2126,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $482$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 1216 530 686
Cusp forms 1024 482 542
Eisenstein series 192 48 144

Trace form

\( 482 q - 3 q^{3} + 226 q^{4} + 5 q^{9} + O(q^{10}) \) \( 482 q - 3 q^{3} + 226 q^{4} + 5 q^{9} - 24 q^{12} - 176 q^{16} + 14 q^{18} + 3 q^{19} - 56 q^{22} - 36 q^{24} - 15 q^{31} + 24 q^{33} - 28 q^{36} - 5 q^{37} + 5 q^{39} + 86 q^{43} + 24 q^{46} - 50 q^{51} + 42 q^{52} + 90 q^{54} + 98 q^{57} - 56 q^{58} + 66 q^{61} - 96 q^{64} + 72 q^{66} + 49 q^{67} - 70 q^{72} + 15 q^{73} - 104 q^{78} - 11 q^{79} - 35 q^{81} + 72 q^{82} - 6 q^{87} + 65 q^{93} - 36 q^{94} - 162 q^{96} - 68 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)