Space of modular forms of level 448 and weight 7

• Label: 448.7
• Level: 448
• Weight: 7
• Dimension: 19762
• Nonzero newspaces: 16
• Sturm bound: 86016
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(86016\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(448))\).

	Total	New	Old
Modular forms	37296	19982	17314
Cusp forms	36432	19762	16670
Eisenstein series	864	220	644

Trace form

19762 * q - 32 * q^2 - 24 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 80 * q^8 - 1498 * q^9 - 32 * q^10 + 2696 * q^11 - 32 * q^12 - 10112 * q^13 - 40 * q^14 - 56 * q^15 - 32 * q^16 + 19496 * q^17 - 32 * q^18 + 7848 * q^19 - 32 * q^20 - 16564 * q^21 + 127360 * q^22 - 26268 * q^23 - 322032 * q^24 - 51158 * q^25 + 21168 * q^26 + 71532 * q^27 + 170960 * q^28 + 132720 * q^29 + 412928 * q^30 - 4 * q^31 - 235632 * q^32 - 355580 * q^33 - 558032 * q^34 - 112448 * q^35 - 730480 * q^36 + 96448 * q^37 + 400368 * q^38 + 508772 * q^39 + 1151248 * q^40 + 350680 * q^41 + 173760 * q^42 - 536028 * q^43 - 962032 * q^44 - 640648 * q^45 - 32 * q^46 - 20 * q^47 - 32 * q^48 + 205850 * q^49 - 1410944 * q^50 - 39260 * q^51 + 2550208 * q^52 + 602176 * q^53 + 2519392 * q^54 - 1396240 * q^55 - 326576 * q^56 - 435656 * q^57 - 3540272 * q^58 + 3622856 * q^59 - 5023328 * q^60 + 393088 * q^61 - 1082368 * q^62 - 36 * q^63 + 2310256 * q^64 - 712596 * q^65 + 6204192 * q^66 - 6283992 * q^67 + 3694528 * q^68 + 1597960 * q^69 + 2271992 * q^70 - 1602112 * q^71 - 1574672 * q^72 - 271912 * q^73 - 5848336 * q^74 + 8034128 * q^75 - 9130400 * q^76 - 324852 * q^77 + 7564480 * q^78 - 3443732 * q^79 + 4180624 * q^80 - 3544402 * q^81 - 13933952 * q^82 - 576664 * q^83 - 5971544 * q^84 + 1602448 * q^85 + 1656688 * q^86 + 4059748 * q^87 + 9391168 * q^88 + 8814744 * q^89 + 22931968 * q^90 + 1714156 * q^91 + 20210752 * q^92 + 4953424 * q^93 + 5017504 * q^94 - 5378692 * q^95 - 7416112 * q^96 - 13102392 * q^97 - 10348960 * q^98 - 10469164 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(448))\)

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
448.7.c	\(\chi_{448}(321, \cdot)\)	448.7.c.a	1	1
		448.7.c.b	1
		448.7.c.c	2
		448.7.c.d	2
		448.7.c.e	4
		448.7.c.f	4
		448.7.c.g	4
		448.7.c.h	4
		448.7.c.i	12
		448.7.c.j	12
		448.7.c.k	24
		448.7.c.l	24
448.7.d	\(\chi_{448}(127, \cdot)\)	448.7.d.a	6	1
		448.7.d.b	12
		448.7.d.c	16
		448.7.d.d	18
		448.7.d.e	20
448.7.g	\(\chi_{448}(351, \cdot)\)	448.7.g.a	24	1
		448.7.g.b	48
448.7.h	\(\chi_{448}(97, \cdot)\)	448.7.h.a	32	1
		448.7.h.b	64
448.7.k	\(\chi_{448}(15, \cdot)\)	n/a	144	2
448.7.l	\(\chi_{448}(209, \cdot)\)	n/a	188	2
448.7.n	\(\chi_{448}(33, \cdot)\)	n/a	192	2
448.7.o	\(\chi_{448}(95, \cdot)\)	n/a	192	2
448.7.r	\(\chi_{448}(191, \cdot)\)	n/a	188	2
448.7.s	\(\chi_{448}(129, \cdot)\)	n/a	188	2
448.7.v	\(\chi_{448}(41, \cdot)\)	None	0	4
448.7.w	\(\chi_{448}(71, \cdot)\)	None	0	4
448.7.y	\(\chi_{448}(79, \cdot)\)	n/a	376	4
448.7.bb	\(\chi_{448}(17, \cdot)\)	n/a	376	4
448.7.be	\(\chi_{448}(43, \cdot)\)	n/a	2304	8
448.7.bf	\(\chi_{448}(13, \cdot)\)	n/a	3056	8
448.7.bg	\(\chi_{448}(73, \cdot)\)	None	0	8
448.7.bj	\(\chi_{448}(23, \cdot)\)	None	0	8
448.7.bk	\(\chi_{448}(5, \cdot)\)	n/a	6112	16
448.7.bl	\(\chi_{448}(11, \cdot)\)	n/a	6112	16

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(448))\) into lower level spaces

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