Space of modular forms of level 243, weight 5, and Character 243.b

• Label: 243.5.b
• Level: $243$
• Weight: $5$
• Character orbit: 243.b
• Rep. character: $\chi_{243}(242,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $10$
• Sturm bound: $135$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	243.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(135\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(243, [\chi])\).

	Total	New	Old
Modular forms	117	48	69
Cusp forms	99	48	51
Eisenstein series	18	0	18

Trace form

48 * q - 384 * q^4 - 39 * q^7 + 15 * q^13 + 3072 * q^16 + 231 * q^19 - 6000 * q^25 + 1248 * q^28 - 2208 * q^31 - 1206 * q^34 - 1551 * q^37 + 4950 * q^40 + 2112 * q^43 - 5418 * q^46 + 19233 * q^49 - 480 * q^52 + 3816 * q^55 - 7200 * q^58 + 2904 * q^61 - 23190 * q^64 - 13080 * q^67 + 10944 * q^70 + 16296 * q^73 - 3414 * q^76 - 17121 * q^79 - 23040 * q^82 + 44352 * q^85 - 6300 * q^88 - 1896 * q^91 + 29340 * q^94 - 65361 * q^97

Decomposition of \(S_{5}^{\mathrm{new}}(243, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
243.5.b.a	$243$	$5$	243.b	3.b	$2$	$1$	$1$	$25.119$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			243.5.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-94\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{4}-94q^{7}+191q^{13}+2^{8}q^{16}+\cdots\)
243.5.b.b	$243$	$5$	243.b	3.b	$2$	$1$	$1$	$25.119$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			243.5.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(23\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{4}+23q^{7}+146q^{13}+2^{8}q^{16}+\cdots\)
243.5.b.c	$243$	$5$	243.b	3.b	$2$	$2$	$2$	$25.119$	\(\Q(\sqrt{-39}) \)	None		✓			243.5.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-32\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-23q^{4}+\beta q^{5}-2^{4}q^{7}+7\beta q^{8}+\cdots\)
243.5.b.d	$243$	$5$	243.b	3.b	$2$	$2$	$2$	$25.119$	\(\Q(\sqrt{-3}) \)	None		✓			243.5.b.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(100\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-11 q^{4}-5\beta q^{5}+50 q^{7}+\cdots\)
243.5.b.e	$243$	$5$	243.b	3.b	$2$	$2$	$2$	$25.119$	\(\Q(\sqrt{-6}) \)	None		✓			243.5.b.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-110\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+10q^{4}-2^{4}\beta q^{5}-55q^{7}+\cdots\)
243.5.b.f	$243$	$5$	243.b	3.b	$2$	$4$	$4$	$25.119$	4.0.2238912.1	None		✓			243.5.b.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(92\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-20+2\beta _{3})q^{4}+(4\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
243.5.b.g	$243$	$5$	243.b	3.b	$2$	$4$	$4$	$25.119$	4.0.16727328.1	None		✓			243.5.b.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(128\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2^{4}+\beta _{3})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
243.5.b.h	$243$	$5$	243.b	3.b	$2$	$4$	$4$	$25.119$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		✓			243.5.b.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-40\)	$2^{4}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-8+\beta _{2})q^{4}+(3\beta _{1}-\beta _{3})q^{5}+\cdots\)
243.5.b.i	$243$	$5$	243.b	3.b	$2$	$4$	$4$	$25.119$	4.0.225816.1	None		✓			243.5.b.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-28\)	$2\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-5+\cdots)q^{7}+\cdots\)
243.5.b.j	$243$	$5$	243.b	3.b	$2$	$24$	$24$	$25.119$		None		✓	✓		243.5.b.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-78\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{5}^{\mathrm{old}}(243, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(243, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)