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Properties

Label 2100.2.ct
Level $2100$
Weight $2$
Character orbit 2100.ct
Rep. character $\chi_{2100}(113,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
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.ct (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 3936 480 3456
Cusp forms 3744 480 3264
Eisenstein series 192 0 192

Trace form

\( 480 q + 4 q^{3} + O(q^{10}) \) \( 480 q + 4 q^{3} - 24 q^{13} - 8 q^{15} - 40 q^{19} - 88 q^{25} - 8 q^{27} + 20 q^{33} - 32 q^{37} + 40 q^{39} + 8 q^{43} - 20 q^{45} + 8 q^{55} + 28 q^{57} + 32 q^{63} + 104 q^{67} + 80 q^{73} + 28 q^{75} + 80 q^{79} - 40 q^{81} + 184 q^{85} + 120 q^{87} + 104 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)