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Properties

Label 2100.4.dr
Level $2100$
Weight $4$
Character orbit 2100.dr
Rep. character $\chi_{2100}(73,\cdot)$
Character field $\Q(\zeta_{60})$
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.dr (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1920\)

Dimensions

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

Total New Old
Modular forms 23232 1920 21312
Cusp forms 22848 1920 20928
Eisenstein series 384 0 384

Trace form

\( 1920 q - 48 q^{5} - 20 q^{7} + O(q^{10}) \) \( 1920 q - 48 q^{5} - 20 q^{7} - 168 q^{15} - 648 q^{23} - 296 q^{25} + 320 q^{29} - 36 q^{33} - 560 q^{35} + 120 q^{37} - 48 q^{43} - 1464 q^{47} - 5280 q^{53} + 1392 q^{57} + 9840 q^{59} - 144 q^{63} - 1528 q^{65} - 80 q^{67} - 2160 q^{73} - 1872 q^{75} + 1848 q^{77} - 19440 q^{81} + 5408 q^{85} + 36 q^{87} - 1824 q^{93} + 6536 q^{95} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)