Space of modular forms of level 135 and weight 11

• Label: 135.11
• Level: 135
• Weight: 11
• Dimension: 4646
• Nonzero newspaces: 9
• Sturm bound: 14256
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 9 \)
Sturm bound:			\(14256\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(135))\).

	Total	New	Old
Modular forms	6600	4742	1858
Cusp forms	6360	4646	1714
Eisenstein series	240	96	144

Trace form

4646 * q - 10 * q^2 - 12 * q^3 + 2862 * q^4 + 9905 * q^5 - 36516 * q^6 + 4474 * q^7 + 4098 * q^8 - 238272 * q^9 + 56361 * q^10 - 431618 * q^11 + 2030190 * q^12 - 1351558 * q^13 - 8538306 * q^14 + 2548515 * q^15 + 7943170 * q^16 + 2438246 * q^17 - 13353918 * q^18 - 4957804 * q^19 - 10729707 * q^20 + 42099600 * q^21 + 24652526 * q^22 - 18284704 * q^23 - 174718824 * q^24 - 37142503 * q^25 + 12096448 * q^26 + 121124964 * q^27 + 148887756 * q^28 - 98409660 * q^29 - 216153141 * q^30 + 41443874 * q^31 + 48176870 * q^32 + 337943166 * q^33 + 501863606 * q^34 - 114732718 * q^35 - 1224640416 * q^36 - 621753240 * q^37 - 596964414 * q^38 + 478507578 * q^39 + 887728873 * q^40 + 1707737278 * q^41 + 1296949212 * q^42 - 481385914 * q^43 - 4491812898 * q^44 + 82103589 * q^45 - 394157386 * q^46 + 4509113222 * q^47 + 4303569078 * q^48 - 461571678 * q^49 - 6637586590 * q^50 - 4454666820 * q^51 + 3220970958 * q^52 + 458771324 * q^53 + 8135450940 * q^54 + 54411762 * q^55 + 5575929174 * q^56 - 2574954072 * q^57 + 109460486 * q^58 + 11027482590 * q^59 - 451061286 * q^60 + 4633053990 * q^61 - 9290012948 * q^62 - 4541563554 * q^63 - 33688299798 * q^64 - 4731705409 * q^65 + 11188998438 * q^66 + 8880613024 * q^67 + 20450191000 * q^68 + 15535528374 * q^69 + 7489519569 * q^70 + 9787160194 * q^71 + 19097705376 * q^72 - 11248320718 * q^73 - 22920580026 * q^74 - 13894396347 * q^75 - 62363611478 * q^76 - 19730037890 * q^77 - 2703327204 * q^78 + 18028745182 * q^79 + 113734861952 * q^80 + 40399770576 * q^81 + 19975799892 * q^82 - 30174728434 * q^83 + 23536213644 * q^84 - 13852106217 * q^85 - 50999384114 * q^86 - 34849963614 * q^87 - 100813110114 * q^88 - 68860474776 * q^89 + 58907592816 * q^90 + 31602938414 * q^91 + 133439710970 * q^92 - 22037061618 * q^93 + 155801594198 * q^94 + 8093833077 * q^95 + 62201973660 * q^96 - 75218832708 * q^97 - 179294618732 * q^98 + 32876789154 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(135))\)

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
135.11.c	\(\chi_{135}(26, \cdot)\)	135.11.c.a	12	1
		135.11.c.b	14
		135.11.c.c	28
135.11.d	\(\chi_{135}(134, \cdot)\)	135.11.d.a	2	1
		135.11.d.b	2
		135.11.d.c	18
		135.11.d.d	18
		135.11.d.e	40
135.11.g	\(\chi_{135}(28, \cdot)\)	n/a	160	2
135.11.h	\(\chi_{135}(44, \cdot)\)	n/a	116	2
135.11.i	\(\chi_{135}(71, \cdot)\)	135.11.i.a	80	2
135.11.l	\(\chi_{135}(37, \cdot)\)	n/a	232	4
135.11.n	\(\chi_{135}(14, \cdot)\)	n/a	1068	6
135.11.o	\(\chi_{135}(11, \cdot)\)	n/a	720	6
135.11.r	\(\chi_{135}(7, \cdot)\)	n/a	2136	12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(135))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(135)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)