Properties

Label 896.2.u
Level $896$
Weight $2$
Character orbit 896.u
Rep. character $\chi_{896}(113,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $96$
Newform subspaces $3$
Sturm bound $256$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 896 = 2^{7} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 896.u (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 3 \)
Sturm bound: \(256\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(896, [\chi])\).

Total New Old
Modular forms 544 96 448
Cusp forms 480 96 384
Eisenstein series 64 0 64

Trace form

\( 96q + O(q^{10}) \) \( 96q + 8q^{23} + 48q^{27} + 48q^{39} + 8q^{43} - 32q^{51} - 16q^{53} - 64q^{55} - 64q^{61} - 40q^{63} - 40q^{67} - 64q^{69} - 64q^{75} - 16q^{77} + 112q^{87} + 128q^{95} + 128q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(896, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
896.2.u.a \(4\) \(7.155\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(-8\) \(0\) \(q+(1+\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2-2\zeta_{8}+\cdots)q^{5}+\cdots\)
896.2.u.b \(40\) \(7.155\) None \(0\) \(-4\) \(8\) \(0\)
896.2.u.c \(52\) \(7.155\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(896, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)