Space of modular forms of level 495 and weight 6

• Label: 495.6
• Level: 495
• Weight: 6
• Dimension: 30582
• Nonzero newspaces: 24
• Sturm bound: 103680
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(103680\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(495))\).

	Total	New	Old
Modular forms	43840	31070	12770
Cusp forms	42560	30582	11978
Eisenstein series	1280	488	792

Trace form

30582 * q + 10 * q^2 - 72 * q^3 - 98 * q^4 + 237 * q^5 + 596 * q^6 - 1044 * q^7 - 4286 * q^8 - 1928 * q^9 + 5698 * q^10 + 3988 * q^11 + 10320 * q^12 - 3972 * q^13 - 9336 * q^14 - 8492 * q^15 - 23430 * q^16 - 16856 * q^17 - 23592 * q^18 + 18804 * q^19 + 33880 * q^20 + 30432 * q^21 + 39672 * q^22 + 11242 * q^23 + 23684 * q^24 + 37783 * q^25 - 27796 * q^26 - 20580 * q^27 - 78432 * q^28 - 41844 * q^29 - 54076 * q^30 - 57698 * q^31 - 146244 * q^32 - 81028 * q^33 - 22656 * q^34 - 972 * q^35 - 77644 * q^36 + 107862 * q^37 + 215948 * q^38 + 84924 * q^39 + 85270 * q^40 + 149576 * q^41 + 205784 * q^42 - 34908 * q^43 + 13660 * q^44 + 134542 * q^45 + 41412 * q^46 + 47748 * q^47 - 184540 * q^48 + 60646 * q^49 - 4660 * q^50 - 219852 * q^51 - 469116 * q^52 - 261276 * q^53 + 97572 * q^54 + 37769 * q^55 + 473488 * q^56 + 50576 * q^57 - 56232 * q^58 - 218798 * q^59 - 286584 * q^60 - 42016 * q^61 + 14948 * q^62 + 72496 * q^63 - 358554 * q^64 + 259258 * q^65 - 915960 * q^66 - 471062 * q^67 - 711288 * q^68 - 313448 * q^69 + 206102 * q^70 + 349202 * q^71 + 1300856 * q^72 + 463472 * q^73 + 957164 * q^74 - 610288 * q^75 - 96124 * q^76 + 789600 * q^77 - 142832 * q^78 + 103100 * q^79 - 523534 * q^80 + 1184480 * q^81 - 2867742 * q^82 + 224840 * q^83 - 25900 * q^84 + 600498 * q^85 - 113470 * q^86 - 1458136 * q^87 + 631532 * q^88 - 1420766 * q^89 + 477084 * q^90 - 16480 * q^91 + 1712528 * q^92 + 2046352 * q^93 + 1851072 * q^94 + 2634978 * q^95 + 5067788 * q^96 + 939938 * q^97 + 885764 * q^98 + 1984812 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(495))\)

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
495.6.a	\(\chi_{495}(1, \cdot)\)	495.6.a.a	3	1
		495.6.a.b	3
		495.6.a.c	3
		495.6.a.d	3
		495.6.a.e	3
		495.6.a.f	3
		495.6.a.g	4
		495.6.a.h	5
		495.6.a.i	5
		495.6.a.j	5
		495.6.a.k	6
		495.6.a.l	6
		495.6.a.m	6
		495.6.a.n	7
		495.6.a.o	10
		495.6.a.p	10
495.6.c	\(\chi_{495}(199, \cdot)\)	n/a	124	1
495.6.d	\(\chi_{495}(494, \cdot)\)	n/a	120	1
495.6.f	\(\chi_{495}(296, \cdot)\)	495.6.f.a	80	1
495.6.i	\(\chi_{495}(166, \cdot)\)	n/a	400	2
495.6.k	\(\chi_{495}(208, \cdot)\)	n/a	296	2
495.6.l	\(\chi_{495}(188, \cdot)\)	n/a	200	2
495.6.n	\(\chi_{495}(91, \cdot)\)	n/a	400	4
495.6.p	\(\chi_{495}(131, \cdot)\)	n/a	480	2
495.6.r	\(\chi_{495}(164, \cdot)\)	n/a	712	2
495.6.u	\(\chi_{495}(34, \cdot)\)	n/a	600	2
495.6.x	\(\chi_{495}(116, \cdot)\)	n/a	320	4
495.6.z	\(\chi_{495}(134, \cdot)\)	n/a	480	4
495.6.ba	\(\chi_{495}(64, \cdot)\)	n/a	592	4
495.6.bc	\(\chi_{495}(23, \cdot)\)	n/a	1200	4
495.6.bf	\(\chi_{495}(43, \cdot)\)	n/a	1424	4
495.6.bg	\(\chi_{495}(16, \cdot)\)	n/a	1920	8
495.6.bi	\(\chi_{495}(53, \cdot)\)	n/a	960	8
495.6.bj	\(\chi_{495}(28, \cdot)\)	n/a	1184	8
495.6.bl	\(\chi_{495}(4, \cdot)\)	n/a	2848	8
495.6.bo	\(\chi_{495}(29, \cdot)\)	n/a	2848	8
495.6.bq	\(\chi_{495}(41, \cdot)\)	n/a	1920	8
495.6.bs	\(\chi_{495}(7, \cdot)\)	n/a	5696	16
495.6.bv	\(\chi_{495}(38, \cdot)\)	n/a	5696	16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(495))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(495)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)