Space of modular forms of level 3, weight 8, and trivial character

• Label: 3.8.a
• Level: $3$
• Weight: $8$
• Character orbit: 3.a
• Rep. character: $\chi_{3}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(3))\).

	Total	New	Old
Modular forms	3	1	2
Cusp forms	1	1	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	Dim
\(+\)	\(1\)

Trace form

q + 6 * q^2 - 27 * q^3 - 92 * q^4 + 390 * q^5 - 162 * q^6 - 64 * q^7 - 1320 * q^8 + 729 * q^9 + 2340 * q^10 - 948 * q^11 + 2484 * q^12 - 5098 * q^13 - 384 * q^14 - 10530 * q^15 + 3856 * q^16 + 28386 * q^17 + 4374 * q^18 - 8620 * q^19 - 35880 * q^20 + 1728 * q^21 - 5688 * q^22 - 15288 * q^23 + 35640 * q^24 + 73975 * q^25 - 30588 * q^26 - 19683 * q^27 + 5888 * q^28 + 36510 * q^29 - 63180 * q^30 - 276808 * q^31 + 192096 * q^32 + 25596 * q^33 + 170316 * q^34 - 24960 * q^35 - 67068 * q^36 + 268526 * q^37 - 51720 * q^38 + 137646 * q^39 - 514800 * q^40 - 629718 * q^41 + 10368 * q^42 + 685772 * q^43 + 87216 * q^44 + 284310 * q^45 - 91728 * q^46 + 583296 * q^47 - 104112 * q^48 - 819447 * q^49 + 443850 * q^50 - 766422 * q^51 + 469016 * q^52 - 428058 * q^53 - 118098 * q^54 - 369720 * q^55 + 84480 * q^56 + 232740 * q^57 + 219060 * q^58 + 1306380 * q^59 + 968760 * q^60 + 300662 * q^61 - 1660848 * q^62 - 46656 * q^63 + 659008 * q^64 - 1988220 * q^65 + 153576 * q^66 - 507244 * q^67 - 2611512 * q^68 + 412776 * q^69 - 149760 * q^70 + 5560632 * q^71 - 962280 * q^72 + 1369082 * q^73 + 1611156 * q^74 - 1997325 * q^75 + 793040 * q^76 + 60672 * q^77 + 825876 * q^78 - 6913720 * q^79 + 1503840 * q^80 + 531441 * q^81 - 3778308 * q^82 - 4376748 * q^83 - 158976 * q^84 + 11070540 * q^85 + 4114632 * q^86 - 985770 * q^87 + 1251360 * q^88 - 8528310 * q^89 + 1705860 * q^90 + 326272 * q^91 + 1406496 * q^92 + 7473816 * q^93 + 3499776 * q^94 - 3361800 * q^95 - 5186592 * q^96 - 8826814 * q^97 - 4916682 * q^98 - 691092 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3
3.8.a.a	$3$	$8$	3.a	1.a	$1$	$1$	$1$	$0.937$	\(\Q\)	None	✓	✓	✓	✓	3.8.a.a	$1$	$0$	\(6\)	\(-27\)	\(390\)	\(-64\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots\)