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

• Label: 418.2.e
• Level: $418$
• Weight: $2$
• Character orbit: 418.e
• Rep. character: $\chi_{418}(45,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $28$
• Newform subspaces: $9$
• Sturm bound: $120$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(120\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	128	28	100
Cusp forms	112	28	84
Eisenstein series	16	0	16

Trace form

\( 28 q + 4 q^{3} - 14 q^{4} + 16 q^{7} - 6 q^{9} + O(q^{10}) \)

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.e.a	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-1\)	\(-2\)	\(-1\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
418.2.e.b	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
418.2.e.c	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots\)
418.2.e.d	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(2\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
418.2.e.e	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(3\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
418.2.e.f	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(2\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
418.2.e.g	$418$	$2$	418.e	19.c	$3$	$4$	$2$	$3.338$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-1+\beta _{1})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
418.2.e.h	$418$	$2$	418.e	19.c	$3$	$6$	$3$	$3.338$	6.0.591408.1	None		$2$	$0$	\(-3\)	\(2\)	\(-2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
418.2.e.i	$418$	$2$	418.e	19.c	$3$	$6$	$3$	$3.338$	6.0.101617200.1	None		$2$	$0$	\(3\)	\(0\)	\(-6\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{4}q^{2}-\beta _{1}q^{3}+(-1+\beta _{4})q^{4}-2\beta _{4}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(418, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)