Properties

Label 34.2.d
Level 34
Weight 2
Character orbit d
Rep. character \(\chi_{34}(9,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 4
Newforms 1
Sturm bound 9
Trace bound 0

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Defining parameters

Level: \( N \) = \( 34 = 2 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 34.d (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newforms: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(34, [\chi])\).

Total New Old
Modular forms 28 4 24
Cusp forms 12 4 8
Eisenstein series 16 0 16

Trace form

\( 4q - 8q^{5} - 4q^{9} + O(q^{10}) \) \( 4q - 8q^{5} - 4q^{9} - 8q^{10} + 4q^{11} + 4q^{12} + 8q^{14} + 8q^{15} - 4q^{16} + 4q^{18} + 8q^{19} + 8q^{22} - 16q^{23} + 4q^{24} + 16q^{25} - 8q^{26} - 12q^{27} - 8q^{28} - 16q^{33} - 16q^{34} - 4q^{36} - 8q^{37} + 16q^{41} + 8q^{42} + 12q^{43} + 8q^{44} + 8q^{45} - 16q^{49} + 12q^{50} + 16q^{51} + 8q^{52} + 8q^{53} + 4q^{54} + 8q^{57} - 4q^{59} - 8q^{60} + 16q^{61} - 8q^{63} - 16q^{65} - 12q^{66} - 24q^{67} - 16q^{70} - 8q^{71} + 8q^{74} - 28q^{75} - 8q^{76} + 8q^{77} - 8q^{79} + 8q^{80} + 20q^{82} + 12q^{83} - 8q^{85} - 24q^{86} + 8q^{87} + 4q^{88} + 32q^{91} - 8q^{93} + 16q^{94} - 12q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(34, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
34.2.d.a \(4\) \(0.271\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(34, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(34, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)