Properties

Label 896.2.e
Level $896$
Weight $2$
Character orbit 896.e
Rep. character $\chi_{896}(447,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $7$
Sturm bound $256$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 896 = 2^{7} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 896.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(256\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\), \(31\)

Dimensions

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

Total New Old
Modular forms 144 32 112
Cusp forms 112 32 80
Eisenstein series 32 0 32

Trace form

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

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.e.a \(4\) \(7.155\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(-8\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1-\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.b \(4\) \(7.155\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(8\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1-\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.c \(4\) \(7.155\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-2-\beta _{2})q^{7}+q^{9}+\cdots\)
896.2.e.d \(4\) \(7.155\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(2+\beta _{2})q^{7}+q^{9}+\cdots\)
896.2.e.e \(4\) \(7.155\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(-8\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(1+\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.f \(4\) \(7.155\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(8\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(1+\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.g \(8\) \(7.155\) 8.0.2517630976.5 \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots\)

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

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