Properties

Label 2100.2.cm
Level $2100$
Weight $2$
Character orbit 2100.cm
Rep. character $\chi_{2100}(121,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $320$
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.cm (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 3936 320 3616
Cusp forms 3744 320 3424
Eisenstein series 192 0 192

Trace form

\( 320 q - 2 q^{5} + 40 q^{9} + O(q^{10}) \) \( 320 q - 2 q^{5} + 40 q^{9} + 6 q^{11} - 4 q^{15} - 12 q^{17} - 8 q^{19} - 24 q^{23} + 24 q^{29} - 6 q^{31} + 4 q^{33} - 20 q^{35} - 20 q^{37} - 36 q^{41} + 120 q^{43} - 2 q^{45} + 20 q^{47} + 36 q^{53} + 16 q^{57} - 24 q^{59} - 28 q^{61} + 2 q^{63} + 2 q^{65} + 32 q^{67} + 32 q^{69} - 32 q^{71} - 36 q^{73} + 8 q^{75} + 20 q^{77} + 12 q^{79} + 40 q^{81} + 88 q^{83} - 156 q^{85} - 8 q^{87} - 58 q^{91} + 32 q^{93} + 38 q^{95} - 84 q^{97} + 8 q^{99} + O(q^{100}) \)

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

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