Properties

Label 34.2.d
Level $34$
Weight $2$
Character orbit 34.d
Rep. character $\chi_{34}(9,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $4$
Newform subspaces $1$
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: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(34, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
34.2.d.a 34.d 17.d $4$ $0.271$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)

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

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