Properties

Label 210.2.x
Level 210
Weight 2
Character orbit x
Rep. character \(\chi_{210}(23,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 64
Newform subspaces 1
Sturm bound 96
Trace bound 0

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Defining parameters

Level: \( N \) = \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 210.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(210, [\chi])\).

Total New Old
Modular forms 224 64 160
Cusp forms 160 64 96
Eisenstein series 64 0 64

Trace form

\( 64q + 8q^{6} + 4q^{7} + O(q^{10}) \) \( 64q + 8q^{6} + 4q^{7} + 4q^{10} - 24q^{15} + 32q^{16} - 8q^{18} + 12q^{21} - 24q^{22} - 8q^{25} - 72q^{27} + 4q^{28} - 12q^{30} + 32q^{31} - 20q^{33} - 24q^{36} - 8q^{37} - 40q^{42} - 64q^{43} - 28q^{45} + 24q^{46} - 16q^{55} + 24q^{57} - 28q^{58} + 8q^{60} + 24q^{61} - 88q^{63} - 16q^{67} - 12q^{70} + 8q^{72} - 56q^{73} + 8q^{75} - 32q^{76} - 16q^{78} + 4q^{81} + 16q^{82} + 32q^{85} + 76q^{87} + 12q^{88} + 40q^{90} - 48q^{91} + 84q^{93} + 4q^{96} + 104q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(210, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
210.2.x.a \(64\) \(1.677\) None \(0\) \(0\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database