Properties

Label 2100.2.db
Level 2100
Weight 2
Character orbit db
Rep. character \(\chi_{2100}(341,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 640
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.db (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 3936 640 3296
Cusp forms 3744 640 3104
Eisenstein series 192 0 192

Trace form

\( 640q + 4q^{7} + O(q^{10}) \) \( 640q + 4q^{7} - 26q^{15} - 6q^{21} - 2q^{25} + 18q^{31} + 45q^{33} + 8q^{37} + 2q^{39} - 32q^{43} + 87q^{45} + 20q^{49} - 12q^{51} - 124q^{57} + 25q^{63} + 16q^{67} - 24q^{73} + 93q^{75} + 28q^{79} - 4q^{81} - 92q^{85} + 18q^{87} - 2q^{91} + 22q^{93} + 32q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database