Space of modular forms of level 495 and weight 3

• Label: 495.3
• Level: 495
• Weight: 3
• Dimension: 12086
• Nonzero newspaces: 24
• Sturm bound: 51840
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(51840\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(495))\).

	Total	New	Old
Modular forms	17920	12570	5350
Cusp forms	16640	12086	4554
Eisenstein series	1280	484	796

Trace form

12086 * q - 34 * q^2 - 36 * q^3 - 26 * q^4 - 25 * q^5 - 52 * q^6 - 60 * q^7 + 2 * q^8 - 20 * q^9 - 4 * q^10 - 30 * q^11 + 24 * q^12 + 56 * q^13 + 28 * q^14 - 68 * q^15 - 238 * q^16 - 176 * q^17 - 120 * q^18 - 190 * q^19 - 142 * q^20 - 96 * q^21 + 136 * q^22 + 306 * q^23 + 428 * q^24 + 433 * q^25 + 1280 * q^26 + 588 * q^27 + 1220 * q^28 + 736 * q^29 + 32 * q^30 - 70 * q^31 - 556 * q^32 - 298 * q^33 - 1240 * q^34 - 1214 * q^35 - 1900 * q^36 - 1046 * q^37 - 2716 * q^38 - 1260 * q^39 - 1074 * q^40 - 1568 * q^41 - 1216 * q^42 - 196 * q^43 - 640 * q^44 - 62 * q^45 + 972 * q^46 + 900 * q^47 + 1004 * q^48 + 1568 * q^49 + 2500 * q^50 + 1476 * q^51 + 2900 * q^52 + 3168 * q^53 + 2892 * q^54 + 641 * q^55 + 4536 * q^56 + 1940 * q^57 + 1208 * q^58 + 1812 * q^59 + 1596 * q^60 + 328 * q^61 + 1096 * q^62 + 496 * q^63 - 1362 * q^64 - 1066 * q^65 - 408 * q^66 - 1554 * q^67 - 3244 * q^68 - 1184 * q^69 - 2666 * q^70 - 3090 * q^71 - 3424 * q^72 - 2452 * q^73 - 6628 * q^74 - 2392 * q^75 - 3664 * q^76 - 4432 * q^77 - 5384 * q^78 - 2084 * q^79 - 5550 * q^80 - 4636 * q^81 - 1102 * q^82 - 3926 * q^83 - 7828 * q^84 - 146 * q^85 - 4846 * q^86 - 3520 * q^87 + 1420 * q^88 - 1030 * q^89 - 1104 * q^90 + 1896 * q^91 + 1316 * q^92 + 904 * q^93 + 3284 * q^94 + 3102 * q^95 + 1148 * q^96 + 1864 * q^97 + 5736 * q^98 + 1572 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(495))\)

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
495.3.b	\(\chi_{495}(406, \cdot)\)	495.3.b.a	8	1
		495.3.b.b	16
		495.3.b.c	16
495.3.e	\(\chi_{495}(386, \cdot)\)	495.3.e.a	24	1
495.3.g	\(\chi_{495}(89, \cdot)\)	495.3.g.a	40	1
495.3.h	\(\chi_{495}(109, \cdot)\)	495.3.h.a	2	1
		495.3.h.b	2
		495.3.h.c	2
		495.3.h.d	4
		495.3.h.e	4
		495.3.h.f	4
		495.3.h.g	16
		495.3.h.h	24
495.3.j	\(\chi_{495}(298, \cdot)\)	495.3.j.a	20	2
		495.3.j.b	40
		495.3.j.c	40
495.3.m	\(\chi_{495}(98, \cdot)\)	495.3.m.a	96	2
495.3.o	\(\chi_{495}(274, \cdot)\)	n/a	280	2
495.3.q	\(\chi_{495}(254, \cdot)\)	n/a	240	2
495.3.s	\(\chi_{495}(56, \cdot)\)	n/a	160	2
495.3.t	\(\chi_{495}(76, \cdot)\)	n/a	192	2
495.3.v	\(\chi_{495}(19, \cdot)\)	n/a	232	4
495.3.w	\(\chi_{495}(179, \cdot)\)	n/a	192	4
495.3.y	\(\chi_{495}(26, \cdot)\)	n/a	128	4
495.3.bb	\(\chi_{495}(46, \cdot)\)	n/a	160	4
495.3.bd	\(\chi_{495}(32, \cdot)\)	n/a	560	4
495.3.be	\(\chi_{495}(67, \cdot)\)	n/a	480	4
495.3.bh	\(\chi_{495}(8, \cdot)\)	n/a	384	8
495.3.bk	\(\chi_{495}(37, \cdot)\)	n/a	464	8
495.3.bm	\(\chi_{495}(61, \cdot)\)	n/a	768	8
495.3.bn	\(\chi_{495}(86, \cdot)\)	n/a	768	8
495.3.bp	\(\chi_{495}(14, \cdot)\)	n/a	1120	8
495.3.br	\(\chi_{495}(79, \cdot)\)	n/a	1120	8
495.3.bt	\(\chi_{495}(58, \cdot)\)	n/a	2240	16
495.3.bu	\(\chi_{495}(2, \cdot)\)	n/a	2240	16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(495))\) into lower level spaces

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