Space of modular forms of level 9 and weight 8

• Label: 9.8
• Level: 9
• Weight: 8
• Dimension: 15
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 48
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 9 = 3^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(9))\).

	Total	New	Old
Modular forms	25	20	5
Cusp forms	17	15	2
Eisenstein series	8	5	3

Trace form

15 * q - 15 * q^2 + 24 * q^3 + 51 * q^4 - 570 * q^5 - 1233 * q^6 + 372 * q^7 + 7242 * q^8 + 990 * q^9 - 8928 * q^10 - 7512 * q^11 + 8052 * q^12 + 6834 * q^13 - 15888 * q^14 - 1188 * q^15 + 6927 * q^16 + 2178 * q^17 + 42876 * q^18 + 82164 * q^19 - 4908 * q^20 - 187224 * q^21 - 271089 * q^22 - 36300 * q^23 + 215469 * q^24 + 106791 * q^25 + 567060 * q^26 + 322272 * q^27 + 202044 * q^28 - 451158 * q^29 - 1112112 * q^30 - 265596 * q^31 - 1241073 * q^32 - 148518 * q^33 + 962253 * q^34 + 2235576 * q^35 + 2501811 * q^36 - 353670 * q^37 - 1900965 * q^38 - 2057316 * q^39 - 1407384 * q^40 - 1101864 * q^41 + 538866 * q^42 + 1109424 * q^43 + 5081898 * q^44 + 2687580 * q^45 - 577656 * q^46 - 2214780 * q^47 - 7434525 * q^48 - 2510343 * q^49 - 2098311 * q^50 + 2525688 * q^51 + 4347570 * q^52 + 3263706 * q^53 + 5816529 * q^54 + 3300624 * q^55 - 1868946 * q^56 - 3071850 * q^57 - 5970924 * q^58 - 3362016 * q^59 + 371484 * q^60 - 4400250 * q^61 + 634020 * q^62 - 2238804 * q^63 + 1845762 * q^64 + 600600 * q^65 + 5754762 * q^66 + 11014032 * q^67 + 4754151 * q^68 - 3002292 * q^69 - 2191518 * q^70 - 3152232 * q^71 - 9638325 * q^72 - 13310430 * q^73 + 8235348 * q^74 + 19174632 * q^75 + 9458877 * q^76 + 3418152 * q^77 - 13339962 * q^78 + 4506564 * q^79 - 39576288 * q^80 - 28538730 * q^81 + 8965494 * q^82 + 13981800 * q^83 + 30090090 * q^84 - 5005044 * q^85 + 30163929 * q^86 + 10290708 * q^87 - 39169269 * q^88 - 16101954 * q^89 - 13660596 * q^90 + 17479176 * q^91 + 37736898 * q^92 + 27331212 * q^93 + 37575864 * q^94 + 13783872 * q^95 - 3404376 * q^96 - 24764568 * q^97 - 90916632 * q^98 - 49382676 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
9.8.a	\(\chi_{9}(1, \cdot)\)	9.8.a.a	1	1
		9.8.a.b	2
9.8.c	\(\chi_{9}(4, \cdot)\)	9.8.c.a	12	2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)