Space of modular forms of level 448 and weight 3

• Label: 448.3
• Level: 448
• Weight: 3
• Dimension: 6514
• Nonzero newspaces: 16
• Sturm bound: 36864
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(36864\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(448))\).

	Total	New	Old
Modular forms	12720	6734	5986
Cusp forms	11856	6514	5342
Eisenstein series	864	220	644

Trace form

6514 * q - 32 * q^2 - 24 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 80 * q^8 - 58 * q^9 - 32 * q^10 - 56 * q^11 - 32 * q^12 - 64 * q^13 - 40 * q^14 - 56 * q^15 - 32 * q^16 - 24 * q^17 - 32 * q^18 + 40 * q^19 - 32 * q^20 + 44 * q^21 + 64 * q^22 + 100 * q^23 + 528 * q^24 + 202 * q^25 + 368 * q^26 + 108 * q^27 + 80 * q^28 - 16 * q^29 + 128 * q^30 - 4 * q^31 - 112 * q^32 - 188 * q^33 - 272 * q^34 - 128 * q^35 - 880 * q^36 - 384 * q^37 - 592 * q^38 - 412 * q^39 - 752 * q^40 - 552 * q^41 - 480 * q^42 - 284 * q^43 - 240 * q^44 - 328 * q^45 - 32 * q^46 - 20 * q^47 - 32 * q^48 - 38 * q^49 - 704 * q^50 + 1060 * q^51 - 1088 * q^52 + 256 * q^53 - 1184 * q^54 + 1520 * q^55 - 432 * q^56 + 376 * q^57 - 752 * q^58 + 904 * q^59 - 608 * q^60 + 192 * q^61 - 64 * q^62 - 36 * q^63 + 112 * q^64 - 276 * q^65 + 480 * q^66 - 1112 * q^67 + 448 * q^68 - 440 * q^69 + 632 * q^70 - 1600 * q^71 + 1264 * q^72 - 552 * q^73 + 1200 * q^74 - 2032 * q^75 + 1632 * q^76 + 108 * q^77 + 2176 * q^78 - 1044 * q^79 + 2704 * q^80 + 878 * q^81 + 2048 * q^82 + 616 * q^83 + 1192 * q^84 + 848 * q^85 + 1840 * q^86 + 868 * q^87 + 1088 * q^88 + 1048 * q^89 + 1408 * q^90 + 748 * q^91 + 832 * q^92 + 1552 * q^93 + 160 * q^94 + 1148 * q^95 - 304 * q^96 + 904 * q^97 - 448 * q^98 + 788 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(448))\)

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
448.3.c	\(\chi_{448}(321, \cdot)\)	448.3.c.a	1	1
		448.3.c.b	1
		448.3.c.c	2
		448.3.c.d	2
		448.3.c.e	4
		448.3.c.f	4
		448.3.c.g	8
		448.3.c.h	8
448.3.d	\(\chi_{448}(127, \cdot)\)	448.3.d.a	2	1
		448.3.d.b	4
		448.3.d.c	4
		448.3.d.d	6
		448.3.d.e	8
448.3.g	\(\chi_{448}(351, \cdot)\)	448.3.g.a	4	1
		448.3.g.b	4
		448.3.g.c	16
448.3.h	\(\chi_{448}(97, \cdot)\)	448.3.h.a	8	1
		448.3.h.b	24
448.3.k	\(\chi_{448}(15, \cdot)\)	448.3.k.a	48	2
448.3.l	\(\chi_{448}(209, \cdot)\)	448.3.l.a	4	2
		448.3.l.b	56
448.3.n	\(\chi_{448}(33, \cdot)\)	448.3.n.a	20	2
		448.3.n.b	20
		448.3.n.c	24
448.3.o	\(\chi_{448}(95, \cdot)\)	448.3.o.a	20	2
		448.3.o.b	20
		448.3.o.c	24
448.3.r	\(\chi_{448}(191, \cdot)\)	448.3.r.a	4	2
		448.3.r.b	4
		448.3.r.c	4
		448.3.r.d	6
		448.3.r.e	6
		448.3.r.f	12
		448.3.r.g	12
		448.3.r.h	12
448.3.s	\(\chi_{448}(129, \cdot)\)	448.3.s.a	2	2
		448.3.s.b	2
		448.3.s.c	4
		448.3.s.d	4
		448.3.s.e	8
		448.3.s.f	8
		448.3.s.g	16
		448.3.s.h	16
448.3.v	\(\chi_{448}(41, \cdot)\)	None	0	4
448.3.w	\(\chi_{448}(71, \cdot)\)	None	0	4
448.3.y	\(\chi_{448}(79, \cdot)\)	n/a	120	4
448.3.bb	\(\chi_{448}(17, \cdot)\)	n/a	120	4
448.3.be	\(\chi_{448}(43, \cdot)\)	n/a	768	8
448.3.bf	\(\chi_{448}(13, \cdot)\)	n/a	1008	8
448.3.bg	\(\chi_{448}(73, \cdot)\)	None	0	8
448.3.bj	\(\chi_{448}(23, \cdot)\)	None	0	8
448.3.bk	\(\chi_{448}(5, \cdot)\)	n/a	2016	16
448.3.bl	\(\chi_{448}(11, \cdot)\)	n/a	2016	16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(448))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(448)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)