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Properties

Label 32.2.g
Level $32$
Weight $2$
Character orbit 32.g
Rep. character $\chi_{32}(5,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $12$
Newform subspaces $2$
Sturm bound $8$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(32, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\( 12 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - 4 q^{11} + 12 q^{12} - 4 q^{13} + 12 q^{14} + 16 q^{16} + 16 q^{18} - 4 q^{19} + 12 q^{20} - 4 q^{21} + 8 q^{22} + 4 q^{23} - 16 q^{24} - 4 q^{25} - 24 q^{26} + 20 q^{27} - 24 q^{28} - 4 q^{29} - 36 q^{30} + 16 q^{31} - 24 q^{32} - 8 q^{33} - 16 q^{34} + 20 q^{35} - 32 q^{36} - 4 q^{37} + 4 q^{38} + 20 q^{39} + 8 q^{40} - 4 q^{41} + 16 q^{42} + 4 q^{43} + 36 q^{44} + 8 q^{45} + 28 q^{46} + 48 q^{48} + 36 q^{50} - 8 q^{51} + 4 q^{52} + 12 q^{53} + 8 q^{54} - 36 q^{55} + 8 q^{56} - 4 q^{57} - 8 q^{58} - 36 q^{59} - 8 q^{60} + 28 q^{61} - 24 q^{62} - 48 q^{63} - 40 q^{64} - 8 q^{65} - 28 q^{66} - 44 q^{67} + 16 q^{68} + 28 q^{69} - 16 q^{70} - 36 q^{71} + 20 q^{72} - 4 q^{73} + 12 q^{74} - 16 q^{75} - 4 q^{76} + 12 q^{77} + 36 q^{78} - 8 q^{80} - 4 q^{82} + 36 q^{83} + 16 q^{84} + 16 q^{85} - 24 q^{86} + 52 q^{87} - 4 q^{89} + 8 q^{90} + 44 q^{91} - 40 q^{92} - 16 q^{93} + 8 q^{94} + 56 q^{95} - 8 q^{97} - 24 q^{98} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.2.g.a 32.g 32.g $4$ $0.256$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
32.2.g.b 32.g 32.g $8$ $0.256$ 8.0.18939904.2 None \(-4\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{8}]$ \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots\)