Space of modular forms of level 1368, weight 2, and Character 1368.e

• Label: 1368.2.e
• Level: $1368$
• Weight: $2$
• Character orbit: 1368.e
• Rep. character: $\chi_{1368}(379,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $7$
• Sturm bound: $480$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(480\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).

	Total	New	Old
Modular forms	248	102	146
Cusp forms	232	98	134
Eisenstein series	16	4	12

Trace form

\( 98 q - 6 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1368.2.e.a	$1368$	$2$	1368.e	152.b	$2$	$2$	$2$	$10.924$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{2}-2q^{4}+2\beta q^{8}-6q^{11}+4q^{16}+\cdots\)
1368.2.e.b	$1368$	$2$	1368.e	152.b	$2$	$4$	$4$	$10.924$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1-\beta _{3})q^{4}+(-1+2\beta _{3})q^{7}+\cdots\)
1368.2.e.c	$1368$	$2$	1368.e	152.b	$2$	$8$	$8$	$10.924$	8.0.\(\cdots\).11	\(\Q(\sqrt{-114}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{8}+\cdots\)
1368.2.e.d	$1368$	$2$	1368.e	152.b	$2$	$8$	$8$	$10.924$	8.0.207360000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{4})q^{4}+2\beta _{4}q^{7}+\cdots\)
1368.2.e.e	$1368$	$2$	1368.e	152.b	$2$	$12$	$12$	$10.924$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{5}-\beta _{8})q^{5}-\beta _{8}q^{7}+\cdots\)
1368.2.e.f	$1368$	$2$	1368.e	152.b	$2$	$24$	$24$	$10.924$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1368.2.e.g	$1368$	$2$	1368.e	152.b	$2$	$40$	$40$	$10.924$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1368, [\chi]) \cong \)