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

• Label: 448.2.q
• Level: $448$
• Weight: $2$
• Character orbit: 448.q
• Rep. character: $\chi_{448}(31,\cdot)$
• 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.q (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

\( 32 q + 16 q^{9} - 16 q^{25} + 16 q^{49} + 32 q^{57} - 48 q^{73} + 32 q^{81} - 144 q^{89}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
448.2.q.a	$448$	$2$	448.q	56.m	$6$	$8$	$4$	$3.577$	\(\Q(i, \sqrt{3}, \sqrt{5})\)	None		✓			448.2.q.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}+\beta _{7})q^{3}+\beta _{6}q^{5}+(2\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
448.2.q.b	$448$	$2$	448.q	56.m	$6$	$12$	$6$	$3.577$	12.0.\(\cdots\).1	None		✓			448.2.q.b	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{3}+(\beta _{6}-\beta _{7})q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots\)
448.2.q.c	$448$	$2$	448.q	56.m	$6$	$12$	$6$	$3.577$	12.0.\(\cdots\).1	None		✓			448.2.q.b	$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{3}+(-\beta _{6}+\beta _{7})q^{5}+(-\beta _{4}+\beta _{10}+\cdots)q^{7}+\cdots\)

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

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