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

• Label: 1368.2.f
• Level: $1368$
• Weight: $2$
• Character orbit: 1368.f
• Rep. character: $\chi_{1368}(1025,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $480$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(480\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(5\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	256	20	236
Cusp forms	224	20	204
Eisenstein series	32	0	32

Trace form

\( 20 q + 8 q^{7} + O(q^{10}) \)

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.f.a	$1368$	$2$	1368.f	57.d	$2$	$2$	$2$	$10.924$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2q^{7}-3\beta q^{11}-2\beta q^{13}+\cdots\)
1368.2.f.b	$1368$	$2$	1368.f	57.d	$2$	$2$	$2$	$10.924$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2q^{7}-3\beta q^{11}+2\beta q^{13}+\cdots\)
1368.2.f.c	$1368$	$2$	1368.f	57.d	$2$	$8$	$8$	$10.924$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}+\beta _{4}q^{7}+(\beta _{3}+\beta _{5})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots\)
1368.2.f.d	$1368$	$2$	1368.f	57.d	$2$	$8$	$8$	$10.924$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}+\beta _{4}q^{7}+(\beta _{3}+\beta _{5})q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)