Space of modular forms of level 459 and weight 3

• Label: 459.3
• Level: 459
• Weight: 3
• Dimension: 11962
• Nonzero newspaces: 15
• Sturm bound: 46656
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 15 \)
Sturm bound:			\(46656\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(459))\).

	Total	New	Old
Modular forms	16032	12442	3590
Cusp forms	15072	11962	3110
Eisenstein series	960	480	480

Trace form

11962 * q - 58 * q^2 - 84 * q^3 - 86 * q^4 - 22 * q^5 - 60 * q^6 - 90 * q^7 - 46 * q^8 - 96 * q^9 - 118 * q^10 - 58 * q^11 - 66 * q^12 - 66 * q^13 - 22 * q^14 - 78 * q^15 - 86 * q^16 - 55 * q^17 - 318 * q^18 - 108 * q^19 - 502 * q^20 - 360 * q^21 - 214 * q^22 - 400 * q^23 - 384 * q^24 - 170 * q^25 - 64 * q^26 + 84 * q^27 - 36 * q^28 + 428 * q^29 + 390 * q^30 - 30 * q^31 + 774 * q^32 + 318 * q^33 - 31 * q^34 + 376 * q^35 + 624 * q^36 - 144 * q^37 + 230 * q^38 - 126 * q^39 + 570 * q^40 - 130 * q^41 - 1068 * q^42 + 26 * q^43 - 574 * q^44 - 1050 * q^45 - 186 * q^46 - 790 * q^47 - 1002 * q^48 - 126 * q^49 - 576 * q^50 - 132 * q^51 - 662 * q^52 - 256 * q^53 + 12 * q^54 - 348 * q^55 - 298 * q^56 + 288 * q^57 - 366 * q^58 + 482 * q^59 + 1596 * q^60 - 82 * q^61 + 584 * q^62 + 1074 * q^63 - 1114 * q^64 + 326 * q^65 + 750 * q^66 - 624 * q^67 - 190 * q^68 - 390 * q^69 - 1294 * q^70 - 694 * q^71 - 1536 * q^72 - 306 * q^73 - 502 * q^74 - 606 * q^75 - 1014 * q^76 - 454 * q^77 - 456 * q^78 - 414 * q^79 + 336 * q^80 - 168 * q^81 + 404 * q^82 + 122 * q^83 + 1080 * q^84 + 1119 * q^85 + 2422 * q^86 + 462 * q^87 + 2986 * q^88 + 944 * q^89 - 672 * q^90 + 1182 * q^91 + 2054 * q^92 - 1278 * q^93 + 2714 * q^94 - 334 * q^95 - 636 * q^96 + 1084 * q^97 - 1012 * q^98 - 1122 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(459))\)

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
459.3.b	\(\chi_{459}(188, \cdot)\)	459.3.b.a	4	1
		459.3.b.b	4
		459.3.b.c	10
		459.3.b.d	12
		459.3.b.e	12
459.3.c	\(\chi_{459}(458, \cdot)\)	459.3.c.a	2	1
		459.3.c.b	2
		459.3.c.c	2
		459.3.c.d	2
		459.3.c.e	10
		459.3.c.f	10
		459.3.c.g	20
459.3.g	\(\chi_{459}(242, \cdot)\)	459.3.g.a	48	2
		459.3.g.b	48
459.3.i	\(\chi_{459}(152, \cdot)\)	459.3.i.a	68	2
459.3.j	\(\chi_{459}(35, \cdot)\)	459.3.j.a	64	2
459.3.k	\(\chi_{459}(26, \cdot)\)	n/a	192	4
459.3.n	\(\chi_{459}(89, \cdot)\)	n/a	136	4
459.3.q	\(\chi_{459}(28, \cdot)\)	n/a	384	8
459.3.s	\(\chi_{459}(86, \cdot)\)	n/a	576	6
459.3.t	\(\chi_{459}(50, \cdot)\)	n/a	636	6
459.3.u	\(\chi_{459}(8, \cdot)\)	n/a	272	8
459.3.w	\(\chi_{459}(38, \cdot)\)	n/a	1272	12
459.3.z	\(\chi_{459}(10, \cdot)\)	n/a	544	16
459.3.bb	\(\chi_{459}(2, \cdot)\)	n/a	2544	24
459.3.bc	\(\chi_{459}(7, \cdot)\)	n/a	5088	48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(459))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(459)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 2}\)