Space of modular forms of level 9 and weight 14

• Label: 9.14
• Level: 9
• Weight: 14
• Dimension: 29
• Nonzero newspaces: 2
• Newform subspaces: 4
• Sturm bound: 84
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 9 = 3^{2} \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(9))\).

	Total	New	Old
Modular forms	43	34	9
Cusp forms	35	29	6
Eisenstein series	8	5	3

Trace form

29 * q + 129 * q^2 - 732 * q^3 - 33133 * q^4 + 41622 * q^5 - 179433 * q^6 - 146432 * q^7 + 1301802 * q^8 + 247716 * q^9 - 4420656 * q^10 + 15884616 * q^11 + 3110244 * q^12 - 41134274 * q^13 + 107572488 * q^14 + 125678088 * q^15 - 205508593 * q^16 - 222338718 * q^17 + 302719140 * q^18 - 223985588 * q^19 + 569416740 * q^20 - 1179453480 * q^21 - 68756985 * q^22 - 787485936 * q^23 + 7227167013 * q^24 - 1646647273 * q^25 - 11753317164 * q^26 - 2661880752 * q^27 + 7790864476 * q^28 + 14561950278 * q^29 - 23828670216 * q^30 - 15592483160 * q^31 + 37912959423 * q^32 + 26485796700 * q^33 + 1398662613 * q^34 - 9831945984 * q^35 - 30678986637 * q^36 + 2584694254 * q^37 - 16692600621 * q^38 - 675795120 * q^39 + 51743897712 * q^40 + 5987048334 * q^41 - 66579812622 * q^42 - 13549495448 * q^43 - 94429324374 * q^44 + 18812710728 * q^45 - 106023241656 * q^46 + 83247969792 * q^47 + 578553075555 * q^48 - 19184963871 * q^49 - 489359271471 * q^50 - 381866937084 * q^51 - 245165031398 * q^52 + 1073805547302 * q^53 - 256421097927 * q^54 - 527387792184 * q^55 + 148934568270 * q^56 + 821568380412 * q^57 + 443077764660 * q^58 + 1063656325536 * q^59 - 474421590252 * q^60 - 656126914826 * q^61 - 3774065915676 * q^62 - 1601282086776 * q^63 + 3550063065410 * q^64 + 859657943316 * q^65 + 1399091420826 * q^66 - 201925131056 * q^67 + 2524363547823 * q^68 + 1195868876544 * q^69 + 171419748066 * q^70 - 8278186512024 * q^71 - 8843735411109 * q^72 - 137272979678 * q^73 + 8304798939612 * q^74 + 5046580890708 * q^75 + 5672421843517 * q^76 + 4612940773584 * q^77 + 4422197495862 * q^78 - 7069576913840 * q^79 - 27874833923712 * q^80 - 8191801732644 * q^81 - 9691445575818 * q^82 + 20452799515044 * q^83 + 34491814005378 * q^84 + 8639087163588 * q^85 + 28458935355633 * q^86 - 10413041553216 * q^87 - 19732823960949 * q^88 - 23838251858478 * q^89 - 48867239563092 * q^90 - 6213049403392 * q^91 + 14200787420754 * q^92 + 62456975369328 * q^93 + 42893814208608 * q^94 + 8851386111024 * q^95 - 40790028862224 * q^96 - 16442680738682 * q^97 - 96955504742448 * q^98 - 61452155792808 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.14.a	\(\chi_{9}(1, \cdot)\)	9.14.a.a	1	1
		9.14.a.b	2
		9.14.a.c	2
9.14.c	\(\chi_{9}(4, \cdot)\)	9.14.c.a	24	2

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)