Properties

Label 128.2.g
Level $128$
Weight $2$
Character orbit 128.g
Rep. character $\chi_{128}(17,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $12$
Newform subspaces $2$
Sturm bound $32$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(128, [\chi])\).

Total New Old
Modular forms 80 20 60
Cusp forms 48 12 36
Eisenstein series 32 8 24

Trace form

\( 12q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 12q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 4q^{23} - 4q^{25} - 20q^{27} - 4q^{29} - 16q^{31} - 8q^{33} - 20q^{35} - 4q^{37} - 20q^{39} - 4q^{41} - 4q^{43} + 8q^{45} + 8q^{51} + 12q^{53} + 36q^{55} - 4q^{57} + 36q^{59} + 28q^{61} + 48q^{63} - 8q^{65} + 44q^{67} + 28q^{69} + 36q^{71} - 4q^{73} + 16q^{75} + 12q^{77} - 36q^{83} + 16q^{85} - 52q^{87} - 4q^{89} - 44q^{91} - 16q^{93} - 56q^{95} - 8q^{97} - 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(128, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
128.2.g.a \(4\) \(1.022\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(-4\) \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
128.2.g.b \(8\) \(1.022\) 8.0.18939904.2 None \(0\) \(4\) \(0\) \(8\) \(q+(\beta _{2}+\beta _{6}-\beta _{7})q^{3}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(128, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(128, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)