Properties

Label 96.3.h
Level $96$
Weight $3$
Character orbit 96.h
Rep. character $\chi_{96}(17,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 96.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(96, [\chi])\).

Total New Old
Modular forms 40 10 30
Cusp forms 24 6 18
Eisenstein series 16 4 12

Trace form

\( 6q + 4q^{7} - 2q^{9} + O(q^{10}) \) \( 6q + 4q^{7} - 2q^{9} + 20q^{15} - 14q^{25} - 60q^{31} - 12q^{33} - 112q^{39} - 30q^{49} + 232q^{55} + 56q^{57} + 260q^{63} + 76q^{73} - 380q^{79} + 38q^{81} - 396q^{87} + 92q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
96.3.h.a \(1\) \(2.616\) \(\Q\) \(\Q(\sqrt{-6}) \) \(0\) \(-3\) \(2\) \(10\) \(q-3q^{3}+2q^{5}+10q^{7}+9q^{9}+10q^{11}+\cdots\)
96.3.h.b \(1\) \(2.616\) \(\Q\) \(\Q(\sqrt{-6}) \) \(0\) \(3\) \(-2\) \(10\) \(q+3q^{3}-2q^{5}+10q^{7}+9q^{9}-10q^{11}+\cdots\)
96.3.h.c \(4\) \(2.616\) \(\Q(\sqrt{2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(-16\) \(q+(-\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{5}-4q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

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