Properties

Label 2100.2.c
Level 2100
Weight 2
Character orbit c
Rep. character \(\chi_{2100}(1651,\cdot)\)
Character field \(\Q\)
Dimension 152
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 504 152 352
Cusp forms 456 152 304
Eisenstein series 48 0 48

Trace form

\( 152q - 2q^{2} + 2q^{4} + 10q^{8} + 152q^{9} + O(q^{10}) \) \( 152q - 2q^{2} + 2q^{4} + 10q^{8} + 152q^{9} + 2q^{14} + 18q^{16} - 2q^{18} - 4q^{21} + 12q^{22} - 10q^{28} - 16q^{29} + 18q^{32} + 2q^{36} - 24q^{37} + 4q^{42} + 8q^{44} + 16q^{46} + 8q^{49} + 32q^{53} + 30q^{56} - 24q^{57} + 60q^{58} + 62q^{64} + 10q^{72} + 72q^{74} + 32q^{77} + 152q^{81} + 8q^{84} - 16q^{86} + 108q^{88} - 100q^{92} + 16q^{93} + 54q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database