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Properties

Label 3675.2.bp
Level $3675$
Weight $2$
Character orbit 3675.bp
Rep. character $\chi_{3675}(97,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1600$
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.bp (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 4608 1600 3008
Cusp forms 4352 1600 2752
Eisenstein series 256 0 256

Trace form

\( 1600 q + 24 q^{8} + O(q^{10}) \) \( 1600 q + 24 q^{8} + 8 q^{15} + 400 q^{16} + 56 q^{22} + 32 q^{23} - 8 q^{25} + 80 q^{29} + 64 q^{30} + 48 q^{32} + 400 q^{36} + 40 q^{37} + 152 q^{43} + 288 q^{50} + 176 q^{53} + 16 q^{57} - 72 q^{58} + 40 q^{60} + 120 q^{64} + 56 q^{65} - 48 q^{67} + 24 q^{72} + 16 q^{78} + 400 q^{81} + 40 q^{85} + 176 q^{88} - 72 q^{92} - 192 q^{93} + 232 q^{95} + O(q^{100}) \)

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

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