Properties

Label 2100.2.cm
Level 2100
Weight 2
Character orbit 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

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

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database