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Properties

Label 2100.2.z
Level $2100$
Weight $2$
Character orbit 2100.z
Rep. character $\chi_{2100}(421,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $128$
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.z (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1968 128 1840
Cusp forms 1872 128 1744
Eisenstein series 96 0 96

Trace form

\( 128 q - 4 q^{5} - 32 q^{9} + O(q^{10}) \) \( 128 q - 4 q^{5} - 32 q^{9} + 4 q^{15} - 8 q^{17} - 12 q^{19} - 4 q^{21} - 12 q^{23} - 20 q^{25} - 36 q^{29} - 12 q^{33} + 4 q^{35} + 4 q^{37} - 24 q^{41} + 16 q^{43} - 4 q^{45} + 48 q^{47} + 128 q^{49} + 32 q^{51} + 24 q^{53} + 20 q^{55} + 8 q^{57} + 24 q^{59} - 48 q^{61} + 36 q^{65} - 24 q^{67} + 8 q^{69} + 64 q^{71} - 8 q^{73} + 16 q^{75} - 24 q^{77} - 16 q^{79} - 32 q^{81} - 12 q^{83} + 4 q^{85} + 24 q^{87} + 60 q^{89} - 8 q^{91} + 48 q^{93} + 44 q^{95} - 28 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)