Properties

Label 3675.2.j
Level $3675$
Weight $2$
Character orbit 3675.j
Rep. character $\chi_{3675}(932,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $472$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 1216 512 704
Cusp forms 1024 472 552
Eisenstein series 192 40 152

Trace form

\( 472 q - 4 q^{3} + 12 q^{6} + O(q^{10}) \) \( 472 q - 4 q^{3} + 12 q^{6} + 16 q^{12} - 8 q^{13} - 396 q^{16} - 4 q^{18} + 40 q^{22} - 16 q^{27} + 4 q^{31} + 28 q^{33} + 4 q^{36} - 24 q^{37} - 16 q^{43} - 104 q^{46} + 16 q^{48} + 8 q^{51} - 8 q^{57} + 16 q^{58} + 108 q^{61} - 152 q^{66} + 24 q^{67} - 52 q^{72} + 32 q^{73} + 72 q^{76} + 152 q^{78} + 64 q^{81} - 80 q^{82} + 4 q^{87} + 192 q^{88} - 24 q^{93} - 156 q^{96} + 24 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)