Space of modular forms of level 448, weight 4, and Character 448.b

• Label: 448.4.b
• Level: $448$
• Weight: $4$
• Character orbit: 448.b
• Rep. character: $\chi_{448}(225,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $6$
• Sturm bound: $256$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(256\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(448, [\chi])\).

	Total	New	Old
Modular forms	204	36	168
Cusp forms	180	36	144
Eisenstein series	24	0	24

Trace form

\( 36 q - 324 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(448, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
448.4.b.a	$448$	$4$	448.b	8.b	$2$	$4$	$4$	$26.433$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-28\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-4\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}-5\zeta_{12}^{3})q^{5}+\cdots\)
448.4.b.b	$448$	$4$	448.b	8.b	$2$	$4$	$4$	$26.433$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(28\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-4\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+5\zeta_{12}^{3})q^{5}+\cdots\)
448.4.b.c	$448$	$4$	448.b	8.b	$2$	$6$	$6$	$26.433$	6.0.819791424.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-42\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{4}-\beta _{5})q^{5}-7q^{7}+\cdots\)
448.4.b.d	$448$	$4$	448.b	8.b	$2$	$6$	$6$	$26.433$	6.0.819791424.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(42\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{4}+\beta _{5})q^{5}+7q^{7}+\cdots\)
448.4.b.e	$448$	$4$	448.b	8.b	$2$	$8$	$8$	$26.433$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-56\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{5}-7q^{7}+(-1+\cdots)q^{9}+\cdots\)
448.4.b.f	$448$	$4$	448.b	8.b	$2$	$8$	$8$	$26.433$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(56\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+7q^{7}+(-1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(448, [\chi]) \cong \)