Space of modular forms of level 1408 and weight 2

• Label: 1408.2
• Level: 1408
• Weight: 2
• Dimension: 33552
• Nonzero newspaces: 20
• Sturm bound: 245760
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 1408 = 2^{7} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(245760\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1408))\).

	Total	New	Old
Modular forms	63040	34416	28624
Cusp forms	59841	33552	26289
Eisenstein series	3199	864	2335

Trace form

33552 * q - 128 * q^2 - 96 * q^3 - 128 * q^4 - 128 * q^5 - 128 * q^6 - 96 * q^7 - 128 * q^8 - 160 * q^9 - 128 * q^10 - 108 * q^11 - 288 * q^12 - 128 * q^13 - 128 * q^14 - 88 * q^15 - 128 * q^16 - 192 * q^17 - 128 * q^18 - 96 * q^19 - 128 * q^20 - 104 * q^21 - 144 * q^22 - 200 * q^23 - 128 * q^24 - 128 * q^25 - 128 * q^26 - 48 * q^27 - 128 * q^28 - 96 * q^29 - 128 * q^30 - 56 * q^31 - 128 * q^32 - 256 * q^33 - 288 * q^34 - 48 * q^35 - 128 * q^36 - 96 * q^37 - 128 * q^38 - 48 * q^39 - 128 * q^40 - 128 * q^41 - 128 * q^42 - 80 * q^43 - 144 * q^44 - 296 * q^45 - 128 * q^46 - 88 * q^47 - 128 * q^48 - 248 * q^49 - 224 * q^50 - 104 * q^51 - 320 * q^52 - 192 * q^53 - 384 * q^54 - 140 * q^55 - 512 * q^56 - 288 * q^57 - 416 * q^58 - 160 * q^59 - 512 * q^60 - 256 * q^61 - 320 * q^62 - 216 * q^63 - 512 * q^64 - 256 * q^65 - 336 * q^66 - 296 * q^67 - 320 * q^68 - 232 * q^69 - 512 * q^70 - 160 * q^71 - 416 * q^72 - 288 * q^73 - 352 * q^74 - 120 * q^75 - 384 * q^76 - 148 * q^77 - 480 * q^78 - 88 * q^79 - 224 * q^80 - 200 * q^81 - 128 * q^82 - 16 * q^83 - 128 * q^84 - 144 * q^85 - 128 * q^86 + 16 * q^87 - 144 * q^88 - 232 * q^89 - 128 * q^90 - 128 * q^92 - 32 * q^93 - 128 * q^94 + 24 * q^95 - 128 * q^96 - 128 * q^97 - 128 * q^98 - 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1408))\)

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
1408.2.a	\(\chi_{1408}(1, \cdot)\)	1408.2.a.a	1	1
		1408.2.a.b	1
		1408.2.a.c	1
		1408.2.a.d	1
		1408.2.a.e	2
		1408.2.a.f	2
		1408.2.a.g	2
		1408.2.a.h	2
		1408.2.a.i	2
		1408.2.a.j	2
		1408.2.a.k	2
		1408.2.a.l	2
		1408.2.a.m	2
		1408.2.a.n	2
		1408.2.a.o	2
		1408.2.a.p	2
		1408.2.a.q	3
		1408.2.a.r	3
		1408.2.a.s	3
		1408.2.a.t	3
1408.2.c	\(\chi_{1408}(705, \cdot)\)	1408.2.c.a	4	1
		1408.2.c.b	4
		1408.2.c.c	6
		1408.2.c.d	6
		1408.2.c.e	8
		1408.2.c.f	12
1408.2.e	\(\chi_{1408}(1407, \cdot)\)	1408.2.e.a	12	1
		1408.2.e.b	12
		1408.2.e.c	12
		1408.2.e.d	12
1408.2.g	\(\chi_{1408}(703, \cdot)\)	1408.2.g.a	4	1
		1408.2.g.b	4
		1408.2.g.c	4
		1408.2.g.d	4
		1408.2.g.e	8
		1408.2.g.f	12
		1408.2.g.g	12
1408.2.i	\(\chi_{1408}(351, \cdot)\)	1408.2.i.a	44	2
		1408.2.i.b	44
1408.2.j	\(\chi_{1408}(353, \cdot)\)	1408.2.j.a	40	2
		1408.2.j.b	40
1408.2.m	\(\chi_{1408}(257, \cdot)\)	n/a	192	4
1408.2.n	\(\chi_{1408}(177, \cdot)\)	n/a	160	4
1408.2.q	\(\chi_{1408}(175, \cdot)\)	n/a	184	4
1408.2.s	\(\chi_{1408}(63, \cdot)\)	n/a	192	4
1408.2.u	\(\chi_{1408}(127, \cdot)\)	n/a	192	4
1408.2.w	\(\chi_{1408}(449, \cdot)\)	n/a	192	4
1408.2.z	\(\chi_{1408}(89, \cdot)\)	None	0	8
1408.2.bb	\(\chi_{1408}(87, \cdot)\)	None	0	8
1408.2.be	\(\chi_{1408}(97, \cdot)\)	n/a	352	8
1408.2.bf	\(\chi_{1408}(95, \cdot)\)	n/a	352	8
1408.2.bg	\(\chi_{1408}(45, \cdot)\)	n/a	2560	16
1408.2.bh	\(\chi_{1408}(43, \cdot)\)	n/a	3040	16
1408.2.bk	\(\chi_{1408}(79, \cdot)\)	n/a	736	16
1408.2.bn	\(\chi_{1408}(49, \cdot)\)	n/a	736	16
1408.2.bo	\(\chi_{1408}(7, \cdot)\)	None	0	32
1408.2.bq	\(\chi_{1408}(9, \cdot)\)	None	0	32
1408.2.bu	\(\chi_{1408}(5, \cdot)\)	n/a	12160	64
1408.2.bv	\(\chi_{1408}(19, \cdot)\)	n/a	12160	64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1408))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1408)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 2}\)