Properties

Label 215.2.g
Level 215
Weight 2
Character orbit g
Rep. character \(\chi_{215}(42,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 40
Newform subspaces 1
Sturm bound 44
Trace bound 0

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Defining parameters

Level: \( N \) = \( 215 = 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 215.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 215 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(44\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(215, [\chi])\).

Total New Old
Modular forms 48 48 0
Cusp forms 40 40 0
Eisenstein series 8 8 0

Trace form

\( 40q - 16q^{6} + O(q^{10}) \) \( 40q - 16q^{6} - 20q^{10} - 8q^{11} + 4q^{13} - 4q^{15} - 20q^{16} - 8q^{17} + 8q^{21} - 28q^{23} - 8q^{25} - 48q^{31} + 24q^{35} + 20q^{36} + 28q^{38} + 68q^{40} + 8q^{41} + 28q^{47} + 8q^{52} + 36q^{53} + 28q^{56} - 36q^{57} + 16q^{58} - 44q^{60} - 52q^{66} - 36q^{67} + 68q^{68} - 132q^{78} + 48q^{81} - 60q^{83} + 12q^{86} - 40q^{87} + 12q^{90} + 168q^{92} + 16q^{95} + 76q^{96} + 20q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(215, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
215.2.g.a \(40\) \(1.717\) None \(0\) \(0\) \(0\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database