Properties

Label 256.2.g
Level $256$
Weight $2$
Character orbit 256.g
Rep. character $\chi_{256}(33,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $24$
Newform subspaces $4$
Sturm bound $64$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 256.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 4 \)
Sturm bound: \(64\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(256, [\chi])\).

Total New Old
Modular forms 160 40 120
Cusp forms 96 24 72
Eisenstein series 64 16 48

Trace form

\( 24q + 8q^{5} - 8q^{9} + O(q^{10}) \) \( 24q + 8q^{5} - 8q^{9} + 8q^{13} + 8q^{21} - 8q^{25} + 8q^{29} - 16q^{33} + 8q^{37} - 8q^{41} - 16q^{45} - 24q^{53} - 8q^{57} - 56q^{61} - 16q^{65} - 56q^{69} - 8q^{73} - 24q^{77} - 32q^{85} - 8q^{89} + 32q^{93} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(256, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
256.2.g.a \(4\) \(2.044\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(-4\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{5}+\cdots\)
256.2.g.b \(4\) \(2.044\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(4\) \(q+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(1+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
256.2.g.c \(8\) \(2.044\) 8.0.18939904.2 None \(0\) \(-4\) \(0\) \(8\) \(q+(-1+\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(\beta _{4}-\beta _{7})q^{5}+\cdots\)
256.2.g.d \(8\) \(2.044\) 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 \(S_{2}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(256, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)