Space of modular forms of level 418, weight 2, and Character 418.m

• Label: 418.2.m
• Level: $418$
• Weight: $2$
• Character orbit: 418.m
• Rep. character: $\chi_{418}(151,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.m (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(418, [\chi])\).

	Total	New	Old
Modular forms	256	80	176
Cusp forms	224	80	144
Eisenstein series	32	0	32

Trace form

\( 80 q - 20 q^{4} + 4 q^{5} + 10 q^{6} - 10 q^{7} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(418, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
418.2.m.a	$418$	$2$	418.m	209.k	$10$	$40$	$10$	$3.338$		None		$2$	$0$	\(-10\)	\(0\)	\(2\)	\(-5\)		$\mathrm{SU}(2)[C_{10}]$
418.2.m.b	$418$	$2$	418.m	209.k	$10$	$40$	$10$	$3.338$		None		$2$	$0$	\(10\)	\(0\)	\(2\)	\(-5\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(418, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(418, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)