Space of modular forms of level 448 and weight 2

• Label: 448.2
• Level: 448
• Weight: 2
• Dimension: 3202
• Nonzero newspaces: 16
• Newform subspaces: 60
• Sturm bound: 24576
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 60 \)
Sturm bound:			\(24576\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(448))\).

	Total	New	Old
Modular forms	6576	3422	3154
Cusp forms	5713	3202	2511
Eisenstein series	863	220	643

Trace form

3202 * q - 32 * q^2 - 24 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 28 * q^7 - 80 * q^8 - 34 * q^9 - 32 * q^10 - 16 * q^11 - 32 * q^12 - 16 * q^13 - 40 * q^14 - 48 * q^15 - 32 * q^16 - 40 * q^17 - 32 * q^18 - 8 * q^19 - 32 * q^20 - 44 * q^21 - 96 * q^22 - 20 * q^23 - 112 * q^24 - 62 * q^25 - 112 * q^26 - 36 * q^27 - 80 * q^28 - 112 * q^29 - 192 * q^30 - 68 * q^31 - 112 * q^32 - 76 * q^33 - 112 * q^34 - 32 * q^35 - 240 * q^36 - 48 * q^37 - 112 * q^38 - 20 * q^39 - 112 * q^40 - 40 * q^41 - 80 * q^42 - 36 * q^43 - 48 * q^44 - 24 * q^45 - 32 * q^46 + 12 * q^47 - 32 * q^48 - 54 * q^49 - 32 * q^50 - 76 * q^51 + 64 * q^52 + 16 * q^53 + 96 * q^54 - 160 * q^55 + 16 * q^56 - 88 * q^57 + 112 * q^58 - 160 * q^59 + 160 * q^60 - 16 * q^61 + 32 * q^62 - 96 * q^63 + 112 * q^64 - 84 * q^65 + 128 * q^66 - 200 * q^67 + 64 * q^68 - 8 * q^69 + 56 * q^70 - 184 * q^71 + 112 * q^72 - 40 * q^73 + 80 * q^74 - 136 * q^75 + 96 * q^76 - 44 * q^77 - 32 * q^78 - 84 * q^79 - 112 * q^80 - 98 * q^81 - 192 * q^82 - 24 * q^83 - 152 * q^84 - 96 * q^85 - 240 * q^86 - 20 * q^87 - 192 * q^88 - 136 * q^89 - 320 * q^90 - 108 * q^91 - 384 * q^92 - 160 * q^93 - 224 * q^94 - 132 * q^95 - 304 * q^96 - 200 * q^97 - 176 * q^98 - 228 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)

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
448.2.a	\(\chi_{448}(1, \cdot)\)	448.2.a.a	1	1
		448.2.a.b	1
		448.2.a.c	1
		448.2.a.d	1
		448.2.a.e	1
		448.2.a.f	1
		448.2.a.g	1
		448.2.a.h	1
		448.2.a.i	2
		448.2.a.j	2
448.2.b	\(\chi_{448}(225, \cdot)\)	448.2.b.a	2	1
		448.2.b.b	2
		448.2.b.c	4
		448.2.b.d	4
448.2.e	\(\chi_{448}(223, \cdot)\)	448.2.e.a	8	1
		448.2.e.b	8
448.2.f	\(\chi_{448}(447, \cdot)\)	448.2.f.a	2	1
		448.2.f.b	2
		448.2.f.c	2
		448.2.f.d	8
448.2.i	\(\chi_{448}(65, \cdot)\)	448.2.i.a	2	2
		448.2.i.b	2
		448.2.i.c	2
		448.2.i.d	2
		448.2.i.e	2
		448.2.i.f	2
		448.2.i.g	4
		448.2.i.h	4
		448.2.i.i	4
		448.2.i.j	4
448.2.j	\(\chi_{448}(111, \cdot)\)	448.2.j.a	4	2
		448.2.j.b	4
		448.2.j.c	4
		448.2.j.d	16
448.2.m	\(\chi_{448}(113, \cdot)\)	448.2.m.a	2	2
		448.2.m.b	2
		448.2.m.c	8
		448.2.m.d	12
448.2.p	\(\chi_{448}(255, \cdot)\)	448.2.p.a	2	2
		448.2.p.b	2
		448.2.p.c	4
		448.2.p.d	4
		448.2.p.e	16
448.2.q	\(\chi_{448}(31, \cdot)\)	448.2.q.a	8	2
		448.2.q.b	12
		448.2.q.c	12
448.2.t	\(\chi_{448}(289, \cdot)\)	448.2.t.a	8	2
		448.2.t.b	12
		448.2.t.c	12
448.2.u	\(\chi_{448}(57, \cdot)\)	None	0	4
448.2.x	\(\chi_{448}(55, \cdot)\)	None	0	4
448.2.z	\(\chi_{448}(47, \cdot)\)	448.2.z.a	56	4
448.2.ba	\(\chi_{448}(81, \cdot)\)	448.2.ba.a	4	4
		448.2.ba.b	4
		448.2.ba.c	48
448.2.bc	\(\chi_{448}(29, \cdot)\)	448.2.bc.a	8	8
		448.2.bc.b	184
		448.2.bc.c	192
448.2.bd	\(\chi_{448}(27, \cdot)\)	448.2.bd.a	16	8
		448.2.bd.b	480
448.2.bh	\(\chi_{448}(9, \cdot)\)	None	0	8
448.2.bi	\(\chi_{448}(87, \cdot)\)	None	0	8
448.2.bm	\(\chi_{448}(3, \cdot)\)	448.2.bm.a	992	16
448.2.bn	\(\chi_{448}(37, \cdot)\)	448.2.bn.a	992	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(448))\) into lower level spaces

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