Space of modular forms of level 27 and weight 9

• Label: 27.9
• Level: 27
• Weight: 9
• Dimension: 163
• Nonzero newspaces: 3
• Newform subspaces: 6
• Sturm bound: 486
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(486\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(27))\).

	Total	New	Old
Modular forms	231	179	52
Cusp forms	201	163	38
Eisenstein series	30	16	14

Trace form

163 * q - 3 * q^2 - 6 * q^3 - 1013 * q^4 - 885 * q^5 - 774 * q^6 + 2033 * q^7 - 9 * q^8 - 12960 * q^9 - 12453 * q^10 + 57345 * q^11 + 77421 * q^12 - 52675 * q^13 - 241941 * q^14 + 105507 * q^15 + 329059 * q^16 - 9 * q^17 - 241317 * q^18 - 177442 * q^19 - 401541 * q^20 + 1164372 * q^21 + 823155 * q^22 + 1068828 * q^23 - 2624256 * q^24 - 840593 * q^25 + 3500568 * q^27 - 2074966 * q^28 - 4741662 * q^29 - 1533627 * q^30 + 1381403 * q^31 + 5456745 * q^32 - 1245285 * q^33 + 7714791 * q^34 + 6225408 * q^35 + 4021128 * q^36 - 13483924 * q^37 - 34684575 * q^38 - 5699685 * q^39 + 8769291 * q^40 + 26933829 * q^41 + 1594134 * q^42 + 19602071 * q^43 + 17341119 * q^44 + 12986721 * q^45 - 32584659 * q^46 - 42490497 * q^47 - 26229183 * q^48 + 15314877 * q^49 + 22900476 * q^50 - 16497396 * q^51 + 45478487 * q^52 + 34106454 * q^54 - 50703990 * q^55 - 64422903 * q^56 + 26766582 * q^57 + 61379655 * q^58 + 159610533 * q^59 - 24031170 * q^60 + 7491869 * q^61 - 223709616 * q^62 - 149069421 * q^63 - 14277131 * q^64 - 48836955 * q^65 + 83336805 * q^66 - 18274048 * q^67 + 179668170 * q^68 + 38038563 * q^69 + 285619155 * q^70 + 125718795 * q^71 + 183269700 * q^72 - 11169475 * q^73 - 56260437 * q^74 - 167459145 * q^75 - 440936209 * q^76 - 399427869 * q^77 - 344470788 * q^78 - 99525565 * q^79 + 151392924 * q^81 + 188410710 * q^82 + 582160659 * q^83 + 836800692 * q^84 + 195550857 * q^85 - 74763939 * q^86 - 145695735 * q^87 - 476974005 * q^88 + 135692730 * q^89 - 821329020 * q^90 - 91011095 * q^91 - 1047793371 * q^92 - 414573177 * q^93 - 40223361 * q^94 + 494286159 * q^95 + 1578184830 * q^96 + 178475174 * q^97 + 1293135102 * q^98 + 228876057 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.9.b	\(\chi_{27}(26, \cdot)\)	27.9.b.a	1	1
		27.9.b.b	2
		27.9.b.c	2
		27.9.b.d	6
27.9.d	\(\chi_{27}(8, \cdot)\)	27.9.d.a	14	2
27.9.f	\(\chi_{27}(2, \cdot)\)	27.9.f.a	138	6

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)