Properties

Label 2100.2.z
Level 2100
Weight 2
Character orbit 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

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

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database