Properties

Label 96.2.d
Level $96$
Weight $2$
Character orbit 96.d
Rep. character $\chi_{96}(49,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 96.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(96, [\chi])\).

Total New Old
Modular forms 24 2 22
Cusp forms 8 2 6
Eisenstein series 16 0 16

Trace form

\( 2q + 4q^{7} - 2q^{9} + O(q^{10}) \) \( 2q + 4q^{7} - 2q^{9} - 4q^{15} - 4q^{17} - 8q^{23} + 2q^{25} - 4q^{31} + 8q^{39} + 4q^{41} + 24q^{47} - 6q^{49} + 8q^{57} - 4q^{63} + 16q^{65} - 24q^{71} - 12q^{73} - 20q^{79} + 2q^{81} + 12q^{87} - 20q^{89} + 16q^{95} - 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
96.2.d.a \(2\) \(0.767\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(4\) \(q+iq^{3}+2iq^{5}+2q^{7}-q^{9}-4iq^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)