Properties

Label 896.2.b
Level $896$
Weight $2$
Character orbit 896.b
Rep. character $\chi_{896}(449,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $8$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(256\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(23\)

Dimensions

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

Total New Old
Modular forms 144 24 120
Cusp forms 112 24 88
Eisenstein series 32 0 32

Trace form

\( 24q - 24q^{9} + O(q^{10}) \) \( 24q - 24q^{9} - 16q^{17} - 8q^{25} + 32q^{33} - 16q^{41} + 24q^{49} - 32q^{57} - 64q^{65} + 48q^{73} + 56q^{81} + 48q^{89} - 16q^{97} + O(q^{100}) \)

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.b.a \(2\) \(7.155\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-iq^{5}-q^{7}-q^{9}-iq^{13}+\cdots\)
896.2.b.b \(2\) \(7.155\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta q^{5}-q^{7}+3q^{9}-\beta q^{11}+\beta q^{13}+\cdots\)
896.2.b.c \(2\) \(7.155\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+iq^{5}+q^{7}-q^{9}+iq^{13}+\cdots\)
896.2.b.d \(2\) \(7.155\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{5}+q^{7}+3q^{9}+\beta q^{11}+\beta q^{13}+\cdots\)
896.2.b.e \(4\) \(7.155\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}+\beta _{1}q^{5}-q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
896.2.b.f \(4\) \(7.155\) 4.0.2048.2 None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(-1-\beta _{3})q^{9}+\cdots\)
896.2.b.g \(4\) \(7.155\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}-\beta _{1}q^{5}+q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
896.2.b.h \(4\) \(7.155\) 4.0.2048.2 None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(-1-\beta _{3})q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)