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

• Label: 1368.2.g
• Level: $1368$
• Weight: $2$
• Character orbit: 1368.g
• Rep. character: $\chi_{1368}(685,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $5$
• Sturm bound: $480$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(480\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	248	90	158
Cusp forms	232	90	142
Eisenstein series	16	0	16

Trace form

\( 90 q - 2 q^{2} + 2 q^{4} - 4 q^{7} + 4 q^{8} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1368.2.g.a	$1368$	$2$	1368.g	8.b	$2$	$2$	$2$	$10.924$	\(\Q(\sqrt{-1}) \)	None					152.2.c.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i+1)q^{2}-2 i q^{4}+2 q^{7}+(-2 i-2)q^{8}+\cdots\)
1368.2.g.b	$1368$	$2$	1368.g	8.b	$2$	$16$	$16$	$10.924$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					152.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots\)
1368.2.g.c	$1368$	$2$	1368.g	8.b	$2$	$18$	$18$	$10.924$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None					456.2.g.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-12\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{14}q^{2}-\beta _{2}q^{4}-\beta _{13}q^{5}+(\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots\)
1368.2.g.d	$1368$	$2$	1368.g	8.b	$2$	$18$	$18$	$10.924$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None					456.2.g.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(20\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}-\beta _{2}q^{4}+\beta _{6}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1368.2.g.e	$1368$	$2$	1368.g	8.b	$2$	$36$	$36$	$10.924$		None		✓	✓		1368.2.g.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1368, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)