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Properties

Label 3675.2.b
Level $3675$
Weight $2$
Character orbit 3675.b
Rep. character $\chi_{3675}(2351,\cdot)$
Character field $\Q$
Dimension $242$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 608 266 342
Cusp forms 512 242 270
Eisenstein series 96 24 72

Trace form

\( 242 q - 236 q^{4} - 2 q^{9} + O(q^{10}) \) \( 242 q - 236 q^{4} - 2 q^{9} + 216 q^{16} - 20 q^{18} + 8 q^{22} - 20 q^{36} - 6 q^{37} - 2 q^{39} - 10 q^{43} + 20 q^{51} + 10 q^{57} + 32 q^{58} - 184 q^{64} - 2 q^{67} + 124 q^{72} + 56 q^{78} + 118 q^{79} + 14 q^{81} - 26 q^{93} + 68 q^{99} + O(q^{100}) \)

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

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