Space of modular forms of level 448 and weight 6

• Label: 448.6
• Level: 448
• Weight: 6
• Dimension: 16450
• Nonzero newspaces: 16
• Sturm bound: 73728
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(73728\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(448))\).

	Total	New	Old
Modular forms	31152	16670	14482
Cusp forms	30288	16450	13838
Eisenstein series	864	220	644

Trace form

16450 * q - 32 * q^2 - 24 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 28 * q^7 - 80 * q^8 + 446 * q^9 - 32 * q^10 - 1232 * q^11 - 32 * q^12 + 432 * q^13 - 40 * q^14 + 3536 * q^15 - 32 * q^16 + 1560 * q^17 - 32 * q^18 - 4744 * q^19 - 32 * q^20 - 5260 * q^21 - 27264 * q^22 - 20 * q^23 + 44048 * q^24 + 31138 * q^25 + 51888 * q^26 + 8412 * q^27 - 4400 * q^28 - 16368 * q^29 - 129792 * q^30 - 23108 * q^31 - 74352 * q^32 - 44428 * q^33 - 25552 * q^34 + 8608 * q^35 + 124560 * q^36 + 46864 * q^37 + 139248 * q^38 - 20 * q^39 + 124688 * q^40 - 26664 * q^41 - 46400 * q^42 - 30820 * q^43 - 131056 * q^44 + 47016 * q^45 - 32 * q^46 + 88332 * q^47 - 32 * q^48 + 29194 * q^49 + 274048 * q^50 - 89036 * q^51 - 147008 * q^52 - 77744 * q^53 - 466592 * q^54 + 440160 * q^55 - 150960 * q^56 - 70808 * q^57 - 52016 * q^58 - 175328 * q^59 + 395680 * q^60 + 100272 * q^61 + 350720 * q^62 - 329696 * q^63 + 749680 * q^64 - 27604 * q^65 + 509216 * q^66 - 395080 * q^67 + 14272 * q^68 - 287048 * q^69 - 286984 * q^70 + 575304 * q^71 - 828176 * q^72 + 169944 * q^73 - 755472 * q^74 + 1082424 * q^75 - 536992 * q^76 + 53236 * q^77 - 665408 * q^78 - 816468 * q^79 + 599696 * q^80 + 408286 * q^81 + 1006208 * q^82 + 455656 * q^83 + 985000 * q^84 + 497888 * q^85 + 1443696 * q^86 - 20 * q^87 + 446528 * q^88 - 230408 * q^89 - 568832 * q^90 - 432876 * q^91 - 1842624 * q^92 - 1837664 * q^93 - 1642592 * q^94 - 616068 * q^95 - 2428720 * q^96 - 146312 * q^97 - 957344 * q^98 + 870236 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(448))\)

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
448.6.a	\(\chi_{448}(1, \cdot)\)	448.6.a.a	1	1
		448.6.a.b	1
		448.6.a.c	1
		448.6.a.d	1
		448.6.a.e	1
		448.6.a.f	1
		448.6.a.g	1
		448.6.a.h	1
		448.6.a.i	1
		448.6.a.j	1
		448.6.a.k	1
		448.6.a.l	1
		448.6.a.m	1
		448.6.a.n	1
		448.6.a.o	1
		448.6.a.p	1
		448.6.a.q	2
		448.6.a.r	2
		448.6.a.s	2
		448.6.a.t	2
		448.6.a.u	2
		448.6.a.v	2
		448.6.a.w	2
		448.6.a.x	2
		448.6.a.y	2
		448.6.a.z	2
		448.6.a.ba	3
		448.6.a.bb	3
		448.6.a.bc	4
		448.6.a.bd	4
		448.6.a.be	5
		448.6.a.bf	5
448.6.b	\(\chi_{448}(225, \cdot)\)	448.6.b.a	10	1
		448.6.b.b	10
		448.6.b.c	20
		448.6.b.d	20
448.6.e	\(\chi_{448}(223, \cdot)\)	448.6.e.a	8	1
		448.6.e.b	16
		448.6.e.c	56
448.6.f	\(\chi_{448}(447, \cdot)\)	448.6.f.a	2	1
		448.6.f.b	8
		448.6.f.c	12
		448.6.f.d	16
		448.6.f.e	40
448.6.i	\(\chi_{448}(65, \cdot)\)	n/a	156	2
448.6.j	\(\chi_{448}(111, \cdot)\)	n/a	156	2
448.6.m	\(\chi_{448}(113, \cdot)\)	n/a	120	2
448.6.p	\(\chi_{448}(255, \cdot)\)	n/a	156	2
448.6.q	\(\chi_{448}(31, \cdot)\)	n/a	160	2
448.6.t	\(\chi_{448}(289, \cdot)\)	n/a	160	2
448.6.u	\(\chi_{448}(57, \cdot)\)	None	0	4
448.6.x	\(\chi_{448}(55, \cdot)\)	None	0	4
448.6.z	\(\chi_{448}(47, \cdot)\)	n/a	312	4
448.6.ba	\(\chi_{448}(81, \cdot)\)	n/a	312	4
448.6.bc	\(\chi_{448}(29, \cdot)\)	n/a	1920	8
448.6.bd	\(\chi_{448}(27, \cdot)\)	n/a	2544	8
448.6.bh	\(\chi_{448}(9, \cdot)\)	None	0	8
448.6.bi	\(\chi_{448}(87, \cdot)\)	None	0	8
448.6.bm	\(\chi_{448}(3, \cdot)\)	n/a	5088	16
448.6.bn	\(\chi_{448}(37, \cdot)\)	n/a	5088	16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(448))\) into lower level spaces

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