Space of modular forms of level 1254, weight 2, and Character 1254.d

• Label: 1254.2.d
• Level: $1254$
• Weight: $2$
• Character orbit: 1254.d
• Rep. character: $\chi_{1254}(683,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1254 = 2 \cdot 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1254.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1254, [\chi])\).

	Total	New	Old
Modular forms	248	64	184
Cusp forms	232	64	168
Eisenstein series	16	0	16

Trace form

64 * q + 64 * q^4 + 24 * q^7 + 64 * q^16 + 20 * q^19 - 48 * q^25 + 24 * q^28 - 16 * q^30 + 60 * q^39 + 12 * q^42 - 40 * q^43 - 96 * q^45 + 16 * q^49 - 12 * q^54 - 12 * q^57 - 8 * q^58 + 88 * q^61 - 4 * q^63 + 64 * q^64 - 104 * q^73 + 20 * q^76 - 24 * q^82 + 32 * q^85 + 52 * q^87 - 64 * q^93

Decomposition of \(S_{2}^{\mathrm{new}}(1254, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1254.2.d.a	$1254$	$2$	1254.d	57.d	$2$	$32$	$32$	$10.013$		None		✓			1254.2.d.a	$2$	$0$	\(-32\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{2}]$
1254.2.d.b	$1254$	$2$	1254.d	57.d	$2$	$32$	$32$	$10.013$		None		✓			1254.2.d.a	$2$	$0$	\(32\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1254, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1254, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(627, [\chi])\)\(^{\oplus 2}\)