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

• Label: 448.2.t
• Level: $448$
• Weight: $2$
• Character orbit: 448.t
• Rep. character: $\chi_{448}(289,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $128$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(128\)
Trace bound:			\(5\)
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	152	32	120
Cusp forms	104	32	72
Eisenstein series	48	0	48

Trace form

\( 32 q + 16 q^{9} + O(q^{10}) \)

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.t.a	$448$	$2$	448.t	56.p	$6$	$8$	$4$	$3.577$	8.0.49787136.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{3}+\beta _{6}q^{5}+(\beta _{5}-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots\)
448.2.t.b	$448$	$2$	448.t	56.p	$6$	$12$	$6$	$3.577$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{10}q^{3}+(-\beta _{2}+\beta _{4}+\beta _{6})q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots\)
448.2.t.c	$448$	$2$	448.t	56.p	$6$	$12$	$6$	$3.577$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{10}q^{3}+(\beta _{2}-\beta _{4}-\beta _{6})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)