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Properties

Label 2100.4.cv
Level $2100$
Weight $4$
Character orbit 2100.cv
Rep. character $\chi_{2100}(89,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1920$
Sturm bound $1920$

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Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2100.cv (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2100, [\chi])\).

Total New Old
Modular forms 11616 1920 9696
Cusp forms 11424 1920 9504
Eisenstein series 192 0 192

Trace form

\( 1920 q + O(q^{10}) \) \( 1920 q - 436 q^{15} + 24 q^{21} + 78 q^{25} - 1242 q^{31} + 2400 q^{33} + 872 q^{39} - 3468 q^{45} - 180 q^{49} + 588 q^{51} - 1450 q^{63} - 6840 q^{73} - 8712 q^{75} + 588 q^{79} - 1124 q^{81} + 6768 q^{85} - 1332 q^{91} - 2368 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

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