Space of modular forms of level 338, weight 2, and Character 338.c

• Label: 338.2.c
• Level: $338$
• Weight: $2$
• Character orbit: 338.c
• Rep. character: $\chi_{338}(191,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $26$
• Newform subspaces: $9$
• Sturm bound: $91$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(91\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(338, [\chi])\).

	Total	New	Old
Modular forms	118	26	92
Cusp forms	62	26	36
Eisenstein series	56	0	56

Trace form

\( 26 q + q^{2} - 13 q^{4} + 2 q^{5} + 4 q^{7} - 2 q^{8} - 17 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(338, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
338.2.c.a	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-1\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.b	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(1\)	\(-6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.c	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(3\)	\(-2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.d	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(-1\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.e	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+4\zeta_{6}q^{7}+\cdots\)
338.2.c.f	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.g	$338$	$2$	338.c	13.c	$3$	$2$	$1$	$2.699$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(3\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.h	$338$	$2$	338.c	13.c	$3$	$6$	$3$	$2.699$	6.0.64827.1	None		$2$	$0$	\(-3\)	\(-3\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
338.2.c.i	$338$	$2$	338.c	13.c	$3$	$6$	$3$	$2.699$	6.0.64827.1	None		$2$	$0$	\(3\)	\(-3\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{5})q^{2}+(-1-\beta _{1}+\beta _{4}+\beta _{5})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(338, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(338, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)