Space of modular forms of level 1240 and weight 2

• Label: 1240.2
• Level: 1240
• Weight: 2
• Dimension: 23362
• Nonzero newspaces: 36
• Sturm bound: 184320
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 1240 = 2^{3} \cdot 5 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(184320\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1240))\).

	Total	New	Old
Modular forms	47520	24058	23462
Cusp forms	44641	23362	21279
Eisenstein series	2879	696	2183

Trace form

23362 * q - 52 * q^2 - 52 * q^3 - 52 * q^4 + 2 * q^5 - 164 * q^6 - 44 * q^7 - 52 * q^8 - 94 * q^9 - 82 * q^10 - 156 * q^11 - 76 * q^12 + 4 * q^13 - 76 * q^14 - 98 * q^15 - 196 * q^16 - 108 * q^17 - 108 * q^18 - 84 * q^19 - 122 * q^20 - 16 * q^21 - 92 * q^22 - 60 * q^23 - 108 * q^24 - 154 * q^25 - 196 * q^26 - 76 * q^27 - 44 * q^28 + 12 * q^29 - 90 * q^30 - 180 * q^31 - 72 * q^32 - 104 * q^33 + 12 * q^34 - 106 * q^35 - 100 * q^36 - 12 * q^37 - 12 * q^38 - 76 * q^39 - 2 * q^40 - 324 * q^41 - 12 * q^42 - 100 * q^43 - 28 * q^44 + 2 * q^45 - 116 * q^46 - 108 * q^47 - 44 * q^48 - 74 * q^49 - 122 * q^50 - 16 * q^51 - 100 * q^52 + 48 * q^53 - 108 * q^54 - 86 * q^55 - 276 * q^56 + 28 * q^57 - 148 * q^58 - 40 * q^59 - 170 * q^60 + 224 * q^61 - 116 * q^62 + 136 * q^63 - 124 * q^64 - 118 * q^65 - 212 * q^66 + 40 * q^67 - 100 * q^68 + 164 * q^69 - 90 * q^70 - 12 * q^71 - 36 * q^72 - 112 * q^73 - 20 * q^74 + 152 * q^75 - 180 * q^76 + 92 * q^77 + 68 * q^78 + 100 * q^79 - 42 * q^80 - 366 * q^81 + 12 * q^82 + 60 * q^83 + 4 * q^84 - 4 * q^85 - 196 * q^86 + 36 * q^87 - 60 * q^88 - 148 * q^89 - 172 * q^90 - 148 * q^91 - 28 * q^92 - 184 * q^94 - 66 * q^95 - 276 * q^96 - 92 * q^97 - 84 * q^98 - 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1240))\)

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
1240.2.a	\(\chi_{1240}(1, \cdot)\)	1240.2.a.a	1	1
		1240.2.a.b	1
		1240.2.a.c	1
		1240.2.a.d	1
		1240.2.a.e	1
		1240.2.a.f	1
		1240.2.a.g	1
		1240.2.a.h	2
		1240.2.a.i	2
		1240.2.a.j	3
		1240.2.a.k	4
		1240.2.a.l	6
		1240.2.a.m	6
1240.2.b	\(\chi_{1240}(371, \cdot)\)	n/a	128	1
1240.2.d	\(\chi_{1240}(249, \cdot)\)	1240.2.d.a	22	1
		1240.2.d.b	22
1240.2.g	\(\chi_{1240}(621, \cdot)\)	n/a	120	1
1240.2.i	\(\chi_{1240}(1239, \cdot)\)	None	0	1
1240.2.j	\(\chi_{1240}(869, \cdot)\)	n/a	180	1
1240.2.l	\(\chi_{1240}(991, \cdot)\)	None	0	1
1240.2.o	\(\chi_{1240}(619, \cdot)\)	n/a	188	1
1240.2.q	\(\chi_{1240}(521, \cdot)\)	1240.2.q.a	2	2
		1240.2.q.b	14
		1240.2.q.c	16
		1240.2.q.d	16
		1240.2.q.e	16
1240.2.r	\(\chi_{1240}(433, \cdot)\)	1240.2.r.a	96	2
1240.2.u	\(\chi_{1240}(63, \cdot)\)	None	0	2
1240.2.v	\(\chi_{1240}(187, \cdot)\)	n/a	360	2
1240.2.y	\(\chi_{1240}(557, \cdot)\)	n/a	376	2
1240.2.z	\(\chi_{1240}(281, \cdot)\)	n/a	128	4
1240.2.bb	\(\chi_{1240}(99, \cdot)\)	n/a	376	2
1240.2.be	\(\chi_{1240}(471, \cdot)\)	None	0	2
1240.2.bg	\(\chi_{1240}(149, \cdot)\)	n/a	376	2
1240.2.bh	\(\chi_{1240}(119, \cdot)\)	None	0	2
1240.2.bj	\(\chi_{1240}(501, \cdot)\)	n/a	256	2
1240.2.bm	\(\chi_{1240}(129, \cdot)\)	1240.2.bm.a	96	2
1240.2.bo	\(\chi_{1240}(491, \cdot)\)	n/a	256	2
1240.2.bq	\(\chi_{1240}(139, \cdot)\)	n/a	752	4
1240.2.bt	\(\chi_{1240}(151, \cdot)\)	None	0	4
1240.2.bv	\(\chi_{1240}(109, \cdot)\)	n/a	752	4
1240.2.bw	\(\chi_{1240}(399, \cdot)\)	None	0	4
1240.2.by	\(\chi_{1240}(101, \cdot)\)	n/a	512	4
1240.2.cb	\(\chi_{1240}(529, \cdot)\)	n/a	192	4
1240.2.cd	\(\chi_{1240}(91, \cdot)\)	n/a	512	4
1240.2.ce	\(\chi_{1240}(37, \cdot)\)	n/a	752	4
1240.2.ch	\(\chi_{1240}(67, \cdot)\)	n/a	752	4
1240.2.ci	\(\chi_{1240}(87, \cdot)\)	None	0	4
1240.2.cl	\(\chi_{1240}(57, \cdot)\)	n/a	192	4
1240.2.cm	\(\chi_{1240}(41, \cdot)\)	n/a	256	8
1240.2.cn	\(\chi_{1240}(77, \cdot)\)	n/a	1504	8
1240.2.cq	\(\chi_{1240}(163, \cdot)\)	n/a	1504	8
1240.2.cr	\(\chi_{1240}(47, \cdot)\)	None	0	8
1240.2.cu	\(\chi_{1240}(153, \cdot)\)	n/a	384	8
1240.2.cv	\(\chi_{1240}(11, \cdot)\)	n/a	1024	8
1240.2.cx	\(\chi_{1240}(9, \cdot)\)	n/a	384	8
1240.2.da	\(\chi_{1240}(381, \cdot)\)	n/a	1024	8
1240.2.dc	\(\chi_{1240}(79, \cdot)\)	None	0	8
1240.2.dd	\(\chi_{1240}(69, \cdot)\)	n/a	1504	8
1240.2.df	\(\chi_{1240}(551, \cdot)\)	None	0	8
1240.2.di	\(\chi_{1240}(179, \cdot)\)	n/a	1504	8
1240.2.dk	\(\chi_{1240}(17, \cdot)\)	n/a	768	16
1240.2.dn	\(\chi_{1240}(7, \cdot)\)	None	0	16
1240.2.do	\(\chi_{1240}(107, \cdot)\)	n/a	3008	16
1240.2.dr	\(\chi_{1240}(13, \cdot)\)	n/a	3008	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 2}\)