Properties

Label 896.2.q
Level $896$
Weight $2$
Character orbit 896.q
Rep. character $\chi_{896}(703,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $4$
Sturm bound $256$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 896 = 2^{7} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 896.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(256\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 288 64 224
Cusp forms 224 64 160
Eisenstein series 64 0 64

Trace form

\( 64q + 32q^{9} + O(q^{10}) \) \( 64q + 32q^{9} - 32q^{25} + 32q^{49} + 64q^{57} - 96q^{73} - 64q^{81} + 96q^{89} + O(q^{100}) \)

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.q.a \(16\) \(7.155\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-12\) \(0\) \(0\) \(q+(-2+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+(\beta _{5}+\beta _{10}+\cdots)q^{5}+\cdots\)
896.2.q.b \(16\) \(7.155\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{13}q^{3}+\beta _{7}q^{5}+(-\beta _{10}+\beta _{14}+\cdots)q^{7}+\cdots\)
896.2.q.c \(16\) \(7.155\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{3}+\beta _{9}q^{5}-\beta _{14}q^{7}+(2\beta _{6}+2\beta _{7}+\cdots)q^{9}+\cdots\)
896.2.q.d \(16\) \(7.155\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(12\) \(0\) \(0\) \(q+(2-\beta _{2}+\beta _{3}-\beta _{7})q^{3}+(\beta _{5}+\beta _{10}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)