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Properties

Label 2100.2.t
Level $2100$
Weight $2$
Character orbit 2100.t
Rep. character $\chi_{2100}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).

Total New Old
Modular forms 1008 216 792
Cusp forms 912 216 696
Eisenstein series 96 0 96

Trace form

\( 216 q - 16 q^{6} + O(q^{10}) \) \( 216 q - 16 q^{6} - 16 q^{12} - 8 q^{13} - 16 q^{16} - 40 q^{17} + 24 q^{22} + 40 q^{32} + 16 q^{36} + 8 q^{37} + 56 q^{38} + 56 q^{46} + 16 q^{52} + 8 q^{53} + 24 q^{56} - 32 q^{58} - 128 q^{61} - 40 q^{62} + 56 q^{68} + 104 q^{73} + 128 q^{76} - 24 q^{78} - 216 q^{81} + 96 q^{82} + 104 q^{86} + 8 q^{88} + 40 q^{92} - 16 q^{93} - 64 q^{96} + 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)