Properties

Label 35.3.l
Level 35
Weight 3
Character orbit l
Rep. character \(\chi_{35}(2,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 24
Newform subspaces 1
Sturm bound 12
Trace bound 0

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(35, [\chi])\).

Total New Old
Modular forms 40 40 0
Cusp forms 24 24 0
Eisenstein series 16 16 0

Trace form

\( 24q - 2q^{2} - 2q^{3} - 4q^{5} - 6q^{7} - 36q^{8} + O(q^{10}) \) \( 24q - 2q^{2} - 2q^{3} - 4q^{5} - 6q^{7} - 36q^{8} + 14q^{10} - 24q^{11} - 46q^{12} - 8q^{13} + 52q^{15} + 20q^{16} - 48q^{17} - 4q^{18} - 72q^{20} + 56q^{21} + 104q^{22} - 86q^{23} - 16q^{25} + 140q^{26} + 76q^{27} + 186q^{28} + 64q^{30} + 120q^{31} + 130q^{32} + 116q^{33} - 240q^{35} - 496q^{36} + 44q^{37} + 16q^{38} - 158q^{40} + 16q^{41} - 370q^{42} - 196q^{43} - 104q^{45} - 148q^{46} - 208q^{47} - 52q^{48} + 580q^{50} - 160q^{51} - 288q^{52} - 72q^{53} + 208q^{55} + 420q^{56} + 656q^{57} - 2q^{58} + 262q^{60} + 308q^{61} + 176q^{62} + 212q^{63} + 132q^{65} + 316q^{66} + 198q^{67} + 332q^{68} - 200q^{70} - 792q^{71} + 308q^{72} + 380q^{73} - 450q^{75} - 400q^{76} - 472q^{77} - 720q^{78} - 324q^{80} - 352q^{81} - 818q^{82} - 460q^{83} + 144q^{85} - 336q^{86} - 214q^{87} - 288q^{88} + 120q^{90} + 984q^{91} + 1372q^{92} - 68q^{93} - 88q^{95} + 816q^{96} - 72q^{97} + 482q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
35.3.l.a \(24\) \(0.954\) None \(-2\) \(-2\) \(-4\) \(-6\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database