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Properties

Label 34.2.c
Level $34$
Weight $2$
Character orbit 34.c
Rep. character $\chi_{34}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $9$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 34 = 2 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 34.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(9\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

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

Trace form

\( 4 q - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + O(q^{10}) \) \( 4 q - 2 q^{3} - 4 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{10} - 6 q^{11} + 2 q^{12} - 4 q^{13} + 4 q^{14} + 4 q^{16} + 6 q^{17} + 4 q^{18} - 2 q^{20} + 8 q^{21} - 10 q^{22} + 8 q^{23} + 2 q^{24} - 8 q^{27} + 4 q^{28} - 10 q^{29} - 8 q^{30} + 4 q^{31} - 4 q^{33} - 6 q^{34} - 16 q^{35} + 6 q^{37} - 16 q^{38} + 12 q^{39} - 6 q^{40} + 4 q^{41} + 6 q^{44} - 2 q^{45} + 8 q^{46} + 32 q^{47} - 2 q^{48} + 12 q^{50} - 6 q^{51} + 4 q^{52} + 8 q^{54} + 24 q^{55} - 4 q^{56} - 8 q^{57} + 2 q^{58} - 26 q^{61} + 20 q^{62} + 4 q^{63} - 4 q^{64} - 32 q^{65} - 28 q^{67} - 6 q^{68} - 16 q^{71} - 4 q^{72} + 8 q^{73} - 6 q^{74} + 6 q^{75} + 12 q^{78} + 2 q^{80} - 8 q^{81} - 8 q^{84} + 22 q^{85} - 4 q^{86} + 10 q^{88} - 10 q^{90} + 24 q^{91} - 8 q^{92} + 24 q^{95} - 2 q^{96} - 4 q^{97} - 16 q^{98} + 22 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
34.2.c.a 34.c 17.c $2$ $0.271$ \(\Q(\sqrt{-1}) \) None 34.2.c.a \(0\) \(-2\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}+(-1-i)q^{3}-q^{4}+(2+2i)q^{5}+\cdots\)
34.2.c.b 34.c 17.c $2$ $0.271$ \(\Q(\sqrt{-1}) \) None 34.2.c.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\)