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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
32.2.g.a \(4\) \(0.256\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(4\) \(q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
32.2.g.b \(8\) \(0.256\) 8.0.18939904.2 None \(-4\) \(-4\) \(0\) \(-8\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots\)