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

• Label: 448.2.ba
• Level: $448$
• Weight: $2$
• Character orbit: 448.ba
• Rep. character: $\chi_{448}(81,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $56$
• Newform subspaces: $3$
• Sturm bound: $128$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.ba (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(128\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	288	72	216
Cusp forms	224	56	168
Eisenstein series	64	16	48

Trace form

56 * q + 2 * q^3 - 2 * q^5 + 6 * q^11 - 8 * q^13 + 16 * q^15 - 4 * q^17 + 2 * q^19 - 10 * q^21 + 20 * q^27 + 8 * q^29 - 20 * q^31 - 4 * q^33 + 2 * q^35 - 10 * q^37 + 16 * q^43 - 28 * q^45 + 44 * q^47 - 8 * q^49 - 30 * q^51 + 6 * q^53 + 18 * q^59 - 2 * q^61 + 36 * q^63 - 4 * q^65 - 30 * q^67 - 20 * q^69 + 24 * q^75 - 18 * q^77 + 4 * q^79 - 8 * q^81 - 32 * q^83 + 12 * q^85 - 32 * q^91 + 10 * q^93 - 20 * q^95 - 16 * q^97 - 8 * q^99

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.ba.a	$448$	$2$	448.ba	112.w	$12$	$4$	$1$	$3.577$	\(\Q(\zeta_{12})\)	None					112.2.w.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-1-\zeta_{12}+\cdots)q^{5}+\cdots\)
448.2.ba.b	$448$	$2$	448.ba	112.w	$12$	$4$	$1$	$3.577$	\(\Q(\zeta_{12})\)	None					112.2.w.a	$2$	$0$	\(0\)	\(4\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12})q^{3}+(-2-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
448.2.ba.c	$448$	$2$	448.ba	112.w	$12$	$48$	$12$	$3.577$		None			✓		112.2.w.c	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(448, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)