Space of modular forms of level 456 and weight 3

• Label: 456.3
• Level: 456
• Weight: 3
• Dimension: 4764
• Nonzero newspaces: 18
• Sturm bound: 34560
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(34560\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(456))\).

	Total	New	Old
Modular forms	11952	4900	7052
Cusp forms	11088	4764	6324
Eisenstein series	864	136	728

Trace form

4764 * q - 4 * q^2 - 22 * q^3 - 12 * q^4 + 10 * q^6 - 4 * q^7 + 8 * q^8 - 28 * q^9 - 12 * q^10 + 64 * q^11 - 50 * q^12 - 40 * q^13 - 72 * q^14 - 42 * q^15 - 100 * q^16 + 16 * q^17 - 142 * q^18 - 72 * q^19 - 144 * q^20 + 24 * q^21 - 132 * q^22 + 86 * q^24 + 72 * q^25 + 192 * q^26 - 16 * q^27 + 316 * q^28 - 288 * q^29 + 326 * q^30 - 284 * q^31 + 176 * q^32 - 292 * q^33 + 100 * q^34 - 336 * q^35 - 234 * q^36 + 24 * q^37 - 40 * q^38 - 192 * q^39 - 532 * q^40 + 64 * q^41 - 458 * q^42 + 4 * q^43 - 128 * q^44 + 304 * q^45 - 340 * q^46 + 360 * q^47 + 126 * q^48 + 560 * q^49 + 236 * q^50 + 556 * q^51 + 284 * q^52 + 386 * q^54 + 556 * q^55 + 336 * q^56 - 48 * q^57 - 80 * q^58 + 256 * q^59 + 426 * q^60 + 848 * q^61 + 1932 * q^62 + 550 * q^63 + 2652 * q^64 + 888 * q^65 + 846 * q^66 + 2196 * q^67 + 1540 * q^68 + 128 * q^69 + 2044 * q^70 + 432 * q^71 + 554 * q^72 - 628 * q^73 + 528 * q^74 - 356 * q^75 - 324 * q^76 - 216 * q^77 - 238 * q^78 - 1844 * q^79 - 1248 * q^80 - 252 * q^81 - 3120 * q^82 - 1184 * q^83 - 2138 * q^84 - 512 * q^85 - 2948 * q^86 - 2298 * q^87 - 3684 * q^88 - 1112 * q^89 - 646 * q^90 - 2676 * q^91 - 3252 * q^92 - 236 * q^93 - 1068 * q^94 + 44 * q^96 + 8 * q^97 - 340 * q^98 + 928 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(456))\)

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
456.3.b	\(\chi_{456}(455, \cdot)\)	None	0	1
456.3.c	\(\chi_{456}(115, \cdot)\)	456.3.c.a	72	1
456.3.h	\(\chi_{456}(305, \cdot)\)	456.3.h.a	36	1
456.3.i	\(\chi_{456}(37, \cdot)\)	456.3.i.a	80	1
456.3.l	\(\chi_{456}(227, \cdot)\)	n/a	156	1
456.3.m	\(\chi_{456}(343, \cdot)\)	None	0	1
456.3.n	\(\chi_{456}(77, \cdot)\)	n/a	144	1
456.3.o	\(\chi_{456}(265, \cdot)\)	456.3.o.a	20	1
456.3.r	\(\chi_{456}(7, \cdot)\)	None	0	2
456.3.s	\(\chi_{456}(107, \cdot)\)	n/a	312	2
456.3.w	\(\chi_{456}(145, \cdot)\)	456.3.w.a	20	2
		456.3.w.b	20
456.3.x	\(\chi_{456}(125, \cdot)\)	n/a	312	2
456.3.ba	\(\chi_{456}(163, \cdot)\)	n/a	160	2
456.3.bb	\(\chi_{456}(335, \cdot)\)	None	0	2
456.3.bc	\(\chi_{456}(373, \cdot)\)	n/a	160	2
456.3.bd	\(\chi_{456}(353, \cdot)\)	456.3.bd.a	80	2
456.3.bh	\(\chi_{456}(5, \cdot)\)	n/a	936	6
456.3.bi	\(\chi_{456}(97, \cdot)\)	n/a	120	6
456.3.bl	\(\chi_{456}(17, \cdot)\)	n/a	240	6
456.3.bn	\(\chi_{456}(13, \cdot)\)	n/a	480	6
456.3.bo	\(\chi_{456}(71, \cdot)\)	None	0	6
456.3.bq	\(\chi_{456}(43, \cdot)\)	n/a	480	6
456.3.bt	\(\chi_{456}(59, \cdot)\)	n/a	936	6
456.3.bv	\(\chi_{456}(55, \cdot)\)	None	0	6

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(456))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(456)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 2}\)