Space of modular forms of level 448 and weight 5

• Label: 448.5
• Level: 448
• Weight: 5
• Dimension: 13138
• Nonzero newspaces: 16
• Sturm bound: 61440
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(61440\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(448))\).

	Total	New	Old
Modular forms	25008	13358	11650
Cusp forms	24144	13138	11006
Eisenstein series	864	220	644

Trace form

13138 * q - 32 * q^2 - 24 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 80 * q^8 - 202 * q^9 - 32 * q^10 + 168 * q^11 - 32 * q^12 + 672 * q^13 - 40 * q^14 - 56 * q^15 - 32 * q^16 - 1016 * q^17 - 32 * q^18 - 1432 * q^19 - 32 * q^20 - 4 * q^21 + 5248 * q^22 + 2276 * q^23 + 528 * q^24 - 1478 * q^25 - 10832 * q^26 - 3348 * q^27 - 5680 * q^28 - 3536 * q^29 - 9472 * q^30 - 4 * q^31 + 5008 * q^32 + 7588 * q^33 + 14128 * q^34 + 1312 * q^35 + 37520 * q^36 + 3104 * q^37 + 15088 * q^38 + 5348 * q^39 - 752 * q^40 + 3032 * q^41 - 16320 * q^42 + 3332 * q^43 - 16880 * q^44 + 3224 * q^45 - 32 * q^46 - 20 * q^47 - 32 * q^48 - 3078 * q^49 - 43136 * q^50 + 26212 * q^51 - 17984 * q^52 - 20192 * q^53 + 31072 * q^54 - 70672 * q^55 + 24656 * q^56 - 19880 * q^57 + 65488 * q^58 - 57816 * q^59 + 63904 * q^60 + 16544 * q^61 + 12032 * q^62 - 36 * q^63 - 24464 * q^64 - 4308 * q^65 - 71136 * q^66 + 91496 * q^67 - 53312 * q^68 + 18856 * q^69 - 61192 * q^70 + 119744 * q^71 - 81680 * q^72 + 35800 * q^73 - 33296 * q^74 + 44336 * q^75 + 28256 * q^76 + 16764 * q^77 + 207808 * q^78 - 100372 * q^79 + 230032 * q^80 - 2290 * q^81 + 10368 * q^82 - 34584 * q^83 - 57944 * q^84 - 83472 * q^85 - 170384 * q^86 - 98588 * q^87 - 142272 * q^88 - 134056 * q^89 - 223232 * q^90 + 748 * q^91 - 159680 * q^92 + 52528 * q^93 - 35936 * q^94 + 76028 * q^95 + 51920 * q^96 + 87848 * q^97 + 76256 * q^98 + 19316 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(448))\)

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
448.5.c	\(\chi_{448}(321, \cdot)\)	448.5.c.a	1	1
		448.5.c.b	1
		448.5.c.c	2
		448.5.c.d	2
		448.5.c.e	4
		448.5.c.f	4
		448.5.c.g	8
		448.5.c.h	8
		448.5.c.i	16
		448.5.c.j	16
448.5.d	\(\chi_{448}(127, \cdot)\)	448.5.d.a	4	1
		448.5.d.b	4
		448.5.d.c	8
		448.5.d.d	8
		448.5.d.e	12
		448.5.d.f	12
448.5.g	\(\chi_{448}(351, \cdot)\)	448.5.g.a	16	1
		448.5.g.b	32
448.5.h	\(\chi_{448}(97, \cdot)\)	448.5.h.a	24	1
		448.5.h.b	40
448.5.k	\(\chi_{448}(15, \cdot)\)	448.5.k.a	96	2
448.5.l	\(\chi_{448}(209, \cdot)\)	n/a	124	2
448.5.n	\(\chi_{448}(33, \cdot)\)	n/a	128	2
448.5.o	\(\chi_{448}(95, \cdot)\)	n/a	128	2
448.5.r	\(\chi_{448}(191, \cdot)\)	n/a	124	2
448.5.s	\(\chi_{448}(129, \cdot)\)	n/a	124	2
448.5.v	\(\chi_{448}(41, \cdot)\)	None	0	4
448.5.w	\(\chi_{448}(71, \cdot)\)	None	0	4
448.5.y	\(\chi_{448}(79, \cdot)\)	n/a	248	4
448.5.bb	\(\chi_{448}(17, \cdot)\)	n/a	248	4
448.5.be	\(\chi_{448}(43, \cdot)\)	n/a	1536	8
448.5.bf	\(\chi_{448}(13, \cdot)\)	n/a	2032	8
448.5.bg	\(\chi_{448}(73, \cdot)\)	None	0	8
448.5.bj	\(\chi_{448}(23, \cdot)\)	None	0	8
448.5.bk	\(\chi_{448}(5, \cdot)\)	n/a	4064	16
448.5.bl	\(\chi_{448}(11, \cdot)\)	n/a	4064	16

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(448))\) into lower level spaces

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