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Properties

Label 3675.2.bv
Level $3675$
Weight $2$
Character orbit 3675.bv
Rep. character $\chi_{3675}(118,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $2016$
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.bv (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(1120\)

Dimensions

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

Total New Old
Modular forms 6864 2016 4848
Cusp forms 6576 2016 4560
Eisenstein series 288 0 288

Trace form

\( 2016 q - 8 q^{7} + 24 q^{8} + O(q^{10}) \) \( 2016 q - 8 q^{7} + 24 q^{8} - 32 q^{11} + 272 q^{16} - 28 q^{17} - 4 q^{21} + 20 q^{22} - 32 q^{23} + 112 q^{26} + 24 q^{28} - 120 q^{32} + 336 q^{36} + 24 q^{37} + 112 q^{41} - 16 q^{42} - 24 q^{43} + 32 q^{46} + 84 q^{47} + 80 q^{51} + 384 q^{56} + 52 q^{58} - 28 q^{61} + 8 q^{63} - 16 q^{67} - 352 q^{71} - 60 q^{72} - 24 q^{77} + 80 q^{78} + 336 q^{81} + 140 q^{82} + 112 q^{83} + 64 q^{86} + 28 q^{87} + 244 q^{88} - 108 q^{91} - 8 q^{92} + 380 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1225, [\chi])\)\(^{\oplus 2}\)