Properties

Label 105.2.u
Level 105
Weight 2
Character orbit u
Rep. character \(\chi_{105}(52,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 32
Newform subspaces 1
Sturm bound 32
Trace bound 0

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Defining parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.u (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

Total New Old
Modular forms 80 32 48
Cusp forms 48 32 16
Eisenstein series 32 0 32

Trace form

\( 32q - 12q^{5} + 8q^{7} - 24q^{8} + O(q^{10}) \) \( 32q - 12q^{5} + 8q^{7} - 24q^{8} - 12q^{10} - 8q^{11} - 8q^{15} - 8q^{21} - 8q^{22} - 8q^{23} + 12q^{25} + 24q^{26} - 24q^{28} + 8q^{30} + 24q^{31} + 24q^{32} - 36q^{33} + 44q^{35} - 32q^{36} + 4q^{37} + 12q^{38} + 12q^{40} + 16q^{42} + 40q^{43} - 40q^{46} - 60q^{47} + 72q^{50} - 8q^{51} - 108q^{52} - 24q^{53} - 48q^{56} + 16q^{57} + 4q^{58} + 20q^{60} - 24q^{61} + 4q^{63} - 4q^{65} + 72q^{66} + 8q^{67} + 132q^{68} + 4q^{70} - 16q^{71} + 12q^{72} + 36q^{73} + 48q^{75} + 60q^{77} + 80q^{78} - 12q^{80} + 16q^{81} + 12q^{82} - 72q^{85} - 16q^{86} - 24q^{87} - 32q^{88} - 24q^{91} - 56q^{92} - 24q^{93} - 12q^{95} - 72q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.2.u.a \(32\) \(0.838\) None \(0\) \(0\) \(-12\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database