Properties

Label 896.2.x
Level $896$
Weight $2$
Character orbit 896.x
Rep. character $\chi_{896}(111,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $120$
Newform subspaces $2$
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.x (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
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 544 136 408
Cusp forms 480 120 360
Eisenstein series 64 16 48

Trace form

\( 120 q + 4 q^{7} - 8 q^{9} + O(q^{10}) \) \( 120 q + 4 q^{7} - 8 q^{9} + 8 q^{11} + 16 q^{15} - 4 q^{21} + 16 q^{23} - 8 q^{25} - 8 q^{29} - 20 q^{35} - 8 q^{37} + 8 q^{39} + 16 q^{43} + 32 q^{51} + 8 q^{53} - 8 q^{57} - 16 q^{65} + 48 q^{67} - 56 q^{71} - 4 q^{77} + 16 q^{79} - 48 q^{85} + 52 q^{91} - 32 q^{93} - 16 q^{99} + O(q^{100}) \)

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.x.a 896.x 224.x $8$ $7.155$ 8.0.157351936.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{8}]$ \(q-\beta _{2}q^{7}-3\beta _{5}q^{9}+(2\beta _{3}+2\beta _{5}-\beta _{6}+\cdots)q^{11}+\cdots\)
896.2.x.b 896.x 224.x $112$ $7.155$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{8}]$

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

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