Space of modular forms of level 9 and weight 4

• Label: 9.4
• Level: 9
• Weight: 4
• Dimension: 5
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 24
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 9 = 3^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(9))\).

	Total	New	Old
Modular forms	13	10	3
Cusp forms	5	5	0
Eisenstein series	8	5	3

Trace form

5 * q - 3 * q^2 - 3 * q^3 - 13 * q^4 - 15 * q^5 + 9 * q^6 + 13 * q^7 + 66 * q^8 + 45 * q^9 + 12 * q^10 - 66 * q^11 - 156 * q^12 - 59 * q^13 - 60 * q^14 + 27 * q^15 + 71 * q^16 + 198 * q^17 + 216 * q^18 - 98 * q^19 + 12 * q^20 + 21 * q^21 + 33 * q^22 - 33 * q^23 - 99 * q^24 - 4 * q^25 - 528 * q^26 - 432 * q^27 + 172 * q^28 + 51 * q^29 + 288 * q^30 + 265 * q^31 + 423 * q^32 + 198 * q^33 - 297 * q^34 + 6 * q^35 - 225 * q^36 + 10 * q^37 + 561 * q^38 + 759 * q^39 - 264 * q^40 - 132 * q^41 - 486 * q^42 - 608 * q^43 - 462 * q^44 - 675 * q^45 - 528 * q^46 - 399 * q^47 - 21 * q^48 + 570 * q^49 + 429 * q^50 + 297 * q^51 + 1330 * q^52 + 108 * q^53 + 1215 * q^54 + 1254 * q^55 - 66 * q^56 - 1221 * q^57 + 60 * q^58 - 798 * q^59 - 36 * q^60 - 257 * q^61 + 228 * q^62 + 603 * q^63 - 1966 * q^64 - 165 * q^65 - 990 * q^66 - 1868 * q^67 - 693 * q^68 + 891 * q^69 - 318 * q^70 + 2736 * q^71 + 891 * q^72 + 280 * q^73 - 816 * q^74 - 363 * q^75 + 1081 * q^76 + 165 * q^77 - 990 * q^78 + 1687 * q^79 + 192 * q^80 - 567 * q^81 + 3630 * q^82 - 813 * q^83 + 642 * q^84 - 594 * q^85 - 33 * q^86 - 153 * q^87 - 1221 * q^88 - 792 * q^89 - 756 * q^90 - 2962 * q^91 + 858 * q^92 - 213 * q^93 - 2100 * q^94 + 132 * q^95 + 1080 * q^96 - 2066 * q^97 - 846 * q^98 + 297 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.4.a	\(\chi_{9}(1, \cdot)\)	9.4.a.a	1	1
9.4.c	\(\chi_{9}(4, \cdot)\)	9.4.c.a	4	2