Space of modular forms of level 1369, weight 2, and Character 1369.b

• Label: 1369.2.b
• Level: $1369$
• Weight: $2$
• Character orbit: 1369.b
• Rep. character: $\chi_{1369}(1368,\cdot)$
• Character field: $\Q$
• Dimension: $94$
• Newform subspaces: $8$
• Sturm bound: $234$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1369 = 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1369.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(234\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1369, [\chi])\).

	Total	New	Old
Modular forms	136	128	8
Cusp forms	98	94	4
Eisenstein series	38	34	4

Trace form

\( 94 q + 2 q^{3} - 74 q^{4} - 6 q^{7} + 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1369, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1369.2.b.a	$1369$	$2$	1369.b	37.b	$2$	$2$	$2$	$10.932$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2q^{4}-q^{7}-2q^{9}-3q^{11}+\cdots\)
1369.2.b.b	$1369$	$2$	1369.b	37.b	$2$	$2$	$2$	$10.932$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}-iq^{5}+2q^{7}+3iq^{8}+\cdots\)
1369.2.b.c	$1369$	$2$	1369.b	37.b	$2$	$2$	$2$	$10.932$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+3q^{3}-2q^{4}-iq^{5}+3iq^{6}+\cdots\)
1369.2.b.d	$1369$	$2$	1369.b	37.b	$2$	$4$	$4$	$10.932$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{3})q^{3}+q^{4}+\cdots\)
1369.2.b.e	$1369$	$2$	1369.b	37.b	$2$	$6$	$6$	$10.932$	6.0.419904.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{2}-\beta _{2}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
1369.2.b.f	$1369$	$2$	1369.b	37.b	$2$	$6$	$6$	$10.932$	6.0.419904.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
1369.2.b.g	$1369$	$2$	1369.b	37.b	$2$	$18$	$18$	$10.932$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(12\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{12})q^{2}+(\beta _{7}-\beta _{15})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1369.2.b.h	$1369$	$2$	1369.b	37.b	$2$	$54$	$54$	$10.932$		None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1369, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1369, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)