Space of modular forms of level 9 and weight 9

• Label: 9.9
• Level: 9
• Weight: 9
• Dimension: 16
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 54
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 9 = 3^{2} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(54\)
Trace bound:			\(1\)

Dimensions

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

	Total	New	Old
Modular forms	28	20	8
Cusp forms	20	16	4
Eisenstein series	8	4	4

Trace form

16 * q - 3 * q^2 - 93 * q^3 + 1243 * q^4 + 438 * q^5 - 2259 * q^6 + 4226 * q^7 + 17973 * q^9 - 8904 * q^10 - 28677 * q^11 - 55110 * q^12 - 50860 * q^13 + 120966 * q^14 - 75276 * q^15 + 38791 * q^16 + 243324 * q^18 - 176350 * q^19 + 539454 * q^20 + 354054 * q^21 + 242607 * q^22 - 1000452 * q^23 - 1125513 * q^24 - 1107977 * q^25 - 524826 * q^27 + 1862060 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 557020 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 526149 * q^34 + 12958047 * q^36 + 3967160 * q^37 + 10967691 * q^38 + 3383976 * q^39 - 3530346 * q^40 - 10239447 * q^41 - 35844228 * q^42 - 3635113 * q^43 + 27631638 * q^45 + 3973488 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 10898031 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 18058192 * q^52 + 36967995 * q^54 + 50349444 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 19430130 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 40066204 * q^61 + 38322432 * q^63 - 6597398 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 36934183 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 13956780 * q^70 + 88821171 * q^72 - 54535666 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 20622319 * q^76 + 56158710 * q^77 + 27355140 * q^78 + 32745866 * q^79 - 16336971 * q^81 + 242093670 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 67465494 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 114516051 * q^88 - 222035850 * q^90 - 288317192 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 50554356 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 78145673 * q^97 - 511060752 * q^99

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

We only show spaces with odd 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
9.9.b	\(\chi_{9}(8, \cdot)\)	9.9.b.a	2	1
9.9.d	\(\chi_{9}(2, \cdot)\)	9.9.d.a	14	2

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

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