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Properties

Label 2100.2.cv
Level $2100$
Weight $2$
Character orbit 2100.cv
Rep. character $\chi_{2100}(89,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $640$
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.cv (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 3936 640 3296
Cusp forms 3744 640 3104
Eisenstein series 192 0 192

Trace form

\( 640 q + O(q^{10}) \) \( 640 q + 38 q^{15} + 6 q^{21} - 6 q^{25} - 18 q^{31} - 75 q^{33} + 2 q^{39} + 87 q^{45} + 20 q^{49} + 12 q^{51} - 25 q^{63} + 120 q^{73} + 99 q^{75} + 28 q^{79} + 4 q^{81} + 84 q^{85} + 2 q^{91} + 32 q^{99} + O(q^{100}) \)

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

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