Space of modular forms of level 270 and weight 11

• Label: 270.11
• Level: 270
• Weight: 11
• Dimension: 4692
• Nonzero newspaces: 9
• Sturm bound: 42768
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 9 \)
Sturm bound:			\(42768\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(270))\).

	Total	New	Old
Modular forms	19680	4692	14988
Cusp forms	19200	4692	14508
Eisenstein series	480	0	480

Trace form

4692 * q + 4096 * q^4 - 19836 * q^5 + 36480 * q^6 - 56632 * q^7 + 476520 * q^9 - 151168 * q^10 - 439368 * q^11 - 67584 * q^12 + 2344488 * q^13 + 702720 * q^14 - 3865842 * q^15 - 2097152 * q^16 - 4876488 * q^17 - 4071936 * q^18 + 10342692 * q^19 + 11848704 * q^20 - 60881736 * q^21 + 387584 * q^22 + 11390316 * q^23 - 10912912 * q^25 - 172172844 * q^27 - 8599552 * q^28 - 4489092 * q^29 + 96350976 * q^30 - 83744448 * q^31 - 144876552 * q^33 - 149507840 * q^34 + 432698238 * q^35 + 318689280 * q^36 + 301059900 * q^37 - 905731200 * q^38 - 827301420 * q^39 - 53411840 * q^40 + 164725848 * q^41 + 979478016 * q^42 + 1055846688 * q^43 - 1345004202 * q^45 - 377628672 * q^46 - 4569079704 * q^47 - 97517568 * q^48 + 1430025072 * q^49 + 6471859200 * q^50 + 4867625316 * q^51 - 1242968064 * q^52 - 4974808488 * q^53 - 1511747712 * q^54 - 458783348 * q^55 - 239861760 * q^56 + 3690123264 * q^57 + 1513143040 * q^58 - 15773348700 * q^59 - 1753168896 * q^60 - 6667096280 * q^61 - 2973178368 * q^62 + 327344124 * q^63 - 15032385536 * q^64 + 8933847888 * q^65 - 7298947584 * q^66 + 2222389484 * q^67 - 3517691904 * q^68 - 3017707092 * q^69 - 7456571200 * q^70 - 34176614496 * q^71 - 12172394496 * q^72 + 10534742584 * q^73 + 20286038016 * q^74 + 10325236926 * q^75 + 14736812032 * q^76 + 38396034120 * q^77 + 11156308992 * q^78 + 28029567456 * q^79 - 38752701144 * q^81 - 10531753984 * q^82 - 40419110352 * q^83 - 20432424960 * q^84 - 5062938348 * q^85 - 23393014272 * q^86 + 99155112396 * q^87 + 31813074944 * q^88 + 120578127336 * q^89 + 42769647360 * q^90 - 64296344712 * q^91 - 20088766464 * q^92 - 128198364324 * q^93 - 124582418560 * q^94 - 33281343528 * q^95 + 2214592512 * q^96 + 135577043700 * q^97 + 141470293248 * q^98 + 66978583836 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(270))\)

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
270.11.b	\(\chi_{270}(269, \cdot)\)	270.11.b.a	20	1
		270.11.b.b	20
		270.11.b.c	40
270.11.d	\(\chi_{270}(161, \cdot)\)	270.11.d.a	12	1
		270.11.d.b	16
		270.11.d.c	24
270.11.g	\(\chi_{270}(163, \cdot)\)	n/a	160	2
270.11.h	\(\chi_{270}(71, \cdot)\)	270.11.h.a	80	2
270.11.j	\(\chi_{270}(89, \cdot)\)	n/a	120	2
270.11.l	\(\chi_{270}(37, \cdot)\)	n/a	240	4
270.11.n	\(\chi_{270}(29, \cdot)\)	n/a	1080	6
270.11.o	\(\chi_{270}(11, \cdot)\)	n/a	720	6
270.11.q	\(\chi_{270}(7, \cdot)\)	n/a	2160	12

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

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(270))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(270)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)