Space of modular forms of level 448, weight 2, and Character 448.j

• Label: 448.2.j
• Level: $448$
• Weight: $2$
• Character orbit: 448.j
• Rep. character: $\chi_{448}(111,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $128$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(448, [\chi])\).

	Total	New	Old
Modular forms	144	36	108
Cusp forms	112	28	84
Eisenstein series	32	8	24

Trace form

\( 28 q + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(448, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
448.2.j.a	$448$	$2$	448.j	112.j	$4$	$4$	$2$	$3.577$	\(\Q(i, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q-\beta _{2}q^{7}+3\beta _{1}q^{9}+(-2+2\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
448.2.j.b	$448$	$2$	448.j	112.j	$4$	$4$	$2$	$3.577$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2})q^{7}-3\beta _{1}q^{9}+\cdots\)
448.2.j.c	$448$	$2$	448.j	112.j	$4$	$4$	$2$	$3.577$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots\)
448.2.j.d	$448$	$2$	448.j	112.j	$4$	$16$	$8$	$3.577$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{3}+\beta _{5}q^{5}+(-1+\beta _{13})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \)