Space of modular forms of level 384, weight 2, and Character 384.k

• Label: 384.2.k
• Level: $384$
• Weight: $2$
• Character orbit: 384.k
• Rep. character: $\chi_{384}(95,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(128\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(384, [\chi])\).

	Total	New	Old
Modular forms	160	40	120
Cusp forms	96	24	72
Eisenstein series	64	16	48

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
384.2.k.a	$384$	$2$	384.k	48.k	$4$	$12$	$6$	$3.066$	12.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(8\)	$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{3}+\beta _{6}q^{5}+(1-\beta _{11})q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots\)
384.2.k.b	$384$	$2$	384.k	48.k	$4$	$12$	$6$	$3.066$	12.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(-8\)	$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{10}q^{3}-\beta _{7}q^{5}+(-1+\beta _{11})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)