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

• Label: 1368.2.s
• Level: $1368$
• Weight: $2$
• Character orbit: 1368.s
• Rep. character: $\chi_{1368}(505,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $50$
• Newform subspaces: $13$
• 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.s (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(480\)
Trace bound:			\(7\)
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	512	50	462
Cusp forms	448	50	398
Eisenstein series	64	0	64

Trace form

50 * q + 4 * q^7 + 2 * q^11 + 4 * q^17 + q^19 + 2 * q^23 - 21 * q^25 - 8 * q^29 - 16 * q^31 - 12 * q^35 + 8 * q^37 - 7 * q^41 + 6 * q^43 - 12 * q^47 + 26 * q^49 + 4 * q^53 - 10 * q^55 + 25 * q^59 + 52 * q^65 - 23 * q^67 + 8 * q^71 - 15 * q^73 - 12 * q^77 - 14 * q^79 + 42 * q^83 - 18 * q^85 + 12 * q^89 + 16 * q^91 - 34 * q^95 + 27 * q^97

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.s.a	$1368$	$2$	1368.s	19.c	$3$	$2$	$1$	$10.924$	\(\Q(\sqrt{-3}) \)	None					152.2.i.b	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+4\zeta_{6})q^{5}-3q^{11}-2\zeta_{6}q^{13}+\cdots\)
1368.2.s.b	$1368$	$2$	1368.s	19.c	$3$	$2$	$1$	$10.924$	\(\Q(\sqrt{-3}) \)	None					456.2.q.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{5}-5q^{7}+4q^{11}-5\zeta_{6}q^{13}+\cdots\)
1368.2.s.c	$1368$	$2$	1368.s	19.c	$3$	$2$	$1$	$10.924$	\(\Q(\sqrt{-3}) \)	None		✓			1368.2.s.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{5}+3q^{7}-6q^{11}+\zeta_{6}q^{13}+\cdots\)
1368.2.s.d	$1368$	$2$	1368.s	19.c	$3$	$2$	$1$	$10.924$	\(\Q(\sqrt{-3}) \)	None					456.2.q.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+3q^{7}-2q^{11}-\zeta_{6}q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
1368.2.s.e	$1368$	$2$	1368.s	19.c	$3$	$2$	$1$	$10.924$	\(\Q(\sqrt{-3}) \)	None					456.2.q.a	$2$	$1$	\(0\)	\(0\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{5}-3q^{7}-5\zeta_{6}q^{13}+(-4+\cdots)q^{17}+\cdots\)
1368.2.s.f	$1368$	$2$	1368.s	19.c	$3$	$2$	$1$	$10.924$	\(\Q(\sqrt{-3}) \)	None		✓			1368.2.s.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{5}+3q^{7}+6q^{11}+\zeta_{6}q^{13}+\cdots\)
1368.2.s.g	$1368$	$2$	1368.s	19.c	$3$	$2$	$1$	$10.924$	\(\Q(\sqrt{-3}) \)	None					152.2.i.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3-3\zeta_{6})q^{5}+4q^{11}+5\zeta_{6}q^{13}+\cdots\)
1368.2.s.h	$1368$	$2$	1368.s	19.c	$3$	$4$	$2$	$10.924$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					456.2.q.d	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{2})q^{5}+(2+\beta _{3})q^{7}+\cdots\)
1368.2.s.i	$1368$	$2$	1368.s	19.c	$3$	$4$	$2$	$10.924$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					456.2.q.e	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(-3+\beta _{3})q^{11}+\cdots\)
1368.2.s.j	$1368$	$2$	1368.s	19.c	$3$	$6$	$3$	$10.924$	\(\Q(\zeta_{18})\)	None					456.2.q.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{5}-\beta_{4})q^{5}+(-\beta_{5}+1)q^{7}+(\beta_{3}-2\beta_1+2)q^{11}+\cdots\)
1368.2.s.k	$1368$	$2$	1368.s	19.c	$3$	$6$	$3$	$10.924$	6.0.2696112.1	None					152.2.i.c	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots\)
1368.2.s.l	$1368$	$2$	1368.s	19.c	$3$	$8$	$4$	$10.924$	8.0.\(\cdots\).5	None		✓			1368.2.s.l	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}+\beta _{5})q^{5}+(-1+\beta _{6})q^{7}+(-1+\cdots)q^{11}+\cdots\)
1368.2.s.m	$1368$	$2$	1368.s	19.c	$3$	$8$	$4$	$10.924$	8.0.\(\cdots\).5	None		✓			1368.2.s.l	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1}+\beta _{3}+\beta _{5})q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1368, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)