Space of modular forms of level 605 and weight 6

• Label: 605.6
• Level: 605
• Weight: 6
• Dimension: 65033
• Nonzero newspaces: 12
• Sturm bound: 174240
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(174240\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(605))\).

	Total	New	Old
Modular forms	73240	65875	7365
Cusp forms	71960	65033	6927
Eisenstein series	1280	842	438

Trace form

65033 * q - 88 * q^2 - 94 * q^3 - 142 * q^4 - 200 * q^5 - 94 * q^6 + 1282 * q^7 + 430 * q^8 - 2823 * q^9 - 2535 * q^10 - 1190 * q^11 - 1338 * q^12 + 2216 * q^13 - 894 * q^14 + 8565 * q^15 + 30418 * q^16 + 5252 * q^17 - 11724 * q^18 - 8410 * q^19 - 17125 * q^20 - 38714 * q^21 - 25240 * q^22 - 37974 * q^23 + 110 * q^24 + 28080 * q^25 + 133666 * q^26 + 95510 * q^27 + 124114 * q^28 - 460 * q^29 - 54845 * q^30 - 90414 * q^31 - 300278 * q^32 - 85320 * q^33 - 11894 * q^34 + 46535 * q^35 + 284738 * q^36 + 137812 * q^37 + 243810 * q^38 + 117874 * q^39 + 95755 * q^40 - 51404 * q^41 - 121726 * q^42 - 149274 * q^43 - 286930 * q^44 - 431380 * q^45 - 370554 * q^46 - 166838 * q^47 - 129014 * q^48 + 172953 * q^49 + 254865 * q^50 + 358006 * q^51 + 272282 * q^52 + 378176 * q^53 + 1148410 * q^54 + 240990 * q^55 + 906890 * q^56 + 225850 * q^57 + 271830 * q^58 + 134730 * q^59 - 463845 * q^60 - 554304 * q^61 - 1229566 * q^62 - 1078414 * q^63 - 1565962 * q^64 - 606815 * q^65 - 242250 * q^66 - 377258 * q^67 + 65114 * q^68 + 457774 * q^69 + 855155 * q^70 - 382494 * q^71 - 114690 * q^72 + 23556 * q^73 + 1459326 * q^74 + 67105 * q^75 + 1114830 * q^76 + 787110 * q^77 + 1665662 * q^78 + 928850 * q^79 - 395765 * q^80 - 1700967 * q^81 - 2280926 * q^82 - 1154034 * q^83 + 387146 * q^84 - 102635 * q^85 + 1131186 * q^86 + 71170 * q^87 + 240700 * q^88 + 317080 * q^89 + 1927545 * q^90 + 506566 * q^91 + 542682 * q^92 - 557458 * q^93 - 1637214 * q^94 - 1340105 * q^95 - 4971834 * q^96 - 697728 * q^97 - 1688716 * q^98 - 527300 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(605))\)

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
605.6.a	\(\chi_{605}(1, \cdot)\)	605.6.a.a	1	1
		605.6.a.b	3
		605.6.a.c	4
		605.6.a.d	5
		605.6.a.e	6
		605.6.a.f	7
		605.6.a.g	7
		605.6.a.h	8
		605.6.a.i	9
		605.6.a.j	9
		605.6.a.k	10
		605.6.a.l	14
		605.6.a.m	18
		605.6.a.n	20
		605.6.a.o	20
		605.6.a.p	20
		605.6.a.q	20
605.6.b	\(\chi_{605}(364, \cdot)\)	n/a	264	1
605.6.e	\(\chi_{605}(362, \cdot)\)	n/a	524	2
605.6.g	\(\chi_{605}(81, \cdot)\)	n/a	720	4
605.6.j	\(\chi_{605}(9, \cdot)\)	n/a	1048	4
605.6.k	\(\chi_{605}(56, \cdot)\)	n/a	2200	10
605.6.m	\(\chi_{605}(112, \cdot)\)	n/a	2096	8
605.6.o	\(\chi_{605}(34, \cdot)\)	n/a	3280	10
605.6.r	\(\chi_{605}(32, \cdot)\)	n/a	6560	20
605.6.s	\(\chi_{605}(16, \cdot)\)	n/a	8800	40
605.6.u	\(\chi_{605}(4, \cdot)\)	n/a	13120	40
605.6.w	\(\chi_{605}(2, \cdot)\)	n/a	26240	80

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(605))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(605)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)