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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
896.2.u.a 896.u 32.g $4$ $7.155$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(1+\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2-2\zeta_{8}+\cdots)q^{5}+\cdots\)
896.2.u.b 896.u 32.g $40$ $7.155$ None \(0\) \(-4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$
896.2.u.c 896.u 32.g $52$ $7.155$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

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

\( S_{2}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)