Space of modular forms of level 495 and weight 4

• Label: 495.4
• Level: 495
• Weight: 4
• Dimension: 18254
• Nonzero newspaces: 24
• Sturm bound: 69120
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(69120\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(495))\).

	Total	New	Old
Modular forms	26560	18742	7818
Cusp forms	25280	18254	7026
Eisenstein series	1280	488	792

Trace form

18254 * q - 26 * q^2 - 36 * q^3 - 90 * q^4 - 57 * q^5 - 52 * q^6 + 38 * q^7 + 34 * q^8 + 28 * q^9 - 406 * q^10 - 314 * q^11 - 432 * q^12 + 162 * q^13 + 1056 * q^14 + 346 * q^15 + 1866 * q^16 + 1402 * q^17 + 840 * q^18 - 1292 * q^19 - 2576 * q^20 - 1140 * q^21 - 2628 * q^22 - 3908 * q^23 - 3388 * q^24 - 169 * q^25 - 1564 * q^26 - 528 * q^27 + 7072 * q^28 + 5550 * q^29 + 4412 * q^30 + 6110 * q^31 + 13692 * q^32 + 4676 * q^33 + 4544 * q^34 + 3573 * q^35 + 3668 * q^36 - 2174 * q^37 - 2308 * q^38 - 660 * q^39 - 8802 * q^40 - 10786 * q^41 - 13576 * q^42 - 9944 * q^43 - 18236 * q^44 - 7214 * q^45 - 6076 * q^46 - 9618 * q^47 - 10876 * q^48 - 836 * q^49 - 2080 * q^50 - 2760 * q^51 - 2940 * q^52 - 3234 * q^53 + 1548 * q^54 + 4527 * q^55 + 13456 * q^56 + 4436 * q^57 + 15616 * q^58 + 11620 * q^59 + 10968 * q^60 + 7838 * q^61 + 31196 * q^62 + 14020 * q^63 + 17718 * q^64 + 9646 * q^65 + 15864 * q^66 + 6100 * q^67 + 18024 * q^68 + 12004 * q^69 - 946 * q^70 + 20882 * q^71 + 18488 * q^72 - 770 * q^73 + 1220 * q^74 + 7790 * q^75 - 7964 * q^76 - 13116 * q^77 - 10112 * q^78 - 10338 * q^79 - 7966 * q^80 + 668 * q^81 - 27930 * q^82 - 9544 * q^83 + 9812 * q^84 - 1741 * q^85 - 20530 * q^86 - 15460 * q^87 - 21732 * q^88 - 37916 * q^89 - 48564 * q^90 - 25774 * q^91 - 64480 * q^92 - 33188 * q^93 - 7552 * q^94 - 20301 * q^95 - 68596 * q^96 - 424 * q^97 - 28588 * q^98 - 31266 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(495))\)

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
495.4.a	\(\chi_{495}(1, \cdot)\)	495.4.a.a	1	1
		495.4.a.b	1
		495.4.a.c	1
		495.4.a.d	2
		495.4.a.e	2
		495.4.a.f	3
		495.4.a.g	3
		495.4.a.h	3
		495.4.a.i	3
		495.4.a.j	3
		495.4.a.k	3
		495.4.a.l	3
		495.4.a.m	4
		495.4.a.n	4
		495.4.a.o	7
		495.4.a.p	7
495.4.c	\(\chi_{495}(199, \cdot)\)	495.4.c.a	6	1
		495.4.c.b	10
		495.4.c.c	14
		495.4.c.d	14
		495.4.c.e	16
		495.4.c.f	16
495.4.d	\(\chi_{495}(494, \cdot)\)	495.4.d.a	16	1
		495.4.d.b	56
495.4.f	\(\chi_{495}(296, \cdot)\)	495.4.f.a	48	1
495.4.i	\(\chi_{495}(166, \cdot)\)	n/a	240	2
495.4.k	\(\chi_{495}(208, \cdot)\)	n/a	176	2
495.4.l	\(\chi_{495}(188, \cdot)\)	n/a	120	2
495.4.n	\(\chi_{495}(91, \cdot)\)	n/a	240	4
495.4.p	\(\chi_{495}(131, \cdot)\)	n/a	288	2
495.4.r	\(\chi_{495}(164, \cdot)\)	n/a	424	2
495.4.u	\(\chi_{495}(34, \cdot)\)	n/a	360	2
495.4.x	\(\chi_{495}(116, \cdot)\)	n/a	192	4
495.4.z	\(\chi_{495}(134, \cdot)\)	n/a	288	4
495.4.ba	\(\chi_{495}(64, \cdot)\)	n/a	352	4
495.4.bc	\(\chi_{495}(23, \cdot)\)	n/a	720	4
495.4.bf	\(\chi_{495}(43, \cdot)\)	n/a	848	4
495.4.bg	\(\chi_{495}(16, \cdot)\)	n/a	1152	8
495.4.bi	\(\chi_{495}(53, \cdot)\)	n/a	576	8
495.4.bj	\(\chi_{495}(28, \cdot)\)	n/a	704	8
495.4.bl	\(\chi_{495}(4, \cdot)\)	n/a	1696	8
495.4.bo	\(\chi_{495}(29, \cdot)\)	n/a	1696	8
495.4.bq	\(\chi_{495}(41, \cdot)\)	n/a	1152	8
495.4.bs	\(\chi_{495}(7, \cdot)\)	n/a	3392	16
495.4.bv	\(\chi_{495}(38, \cdot)\)	n/a	3392	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(495))\) into lower level spaces

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