Space of modular forms of level 1300 and weight 2

• Label: 1300.2
• Level: 1300
• Weight: 2
• Dimension: 26323
• Nonzero newspaces: 40
• Sturm bound: 201600
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(201600\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1300))\).

	Total	New	Old
Modular forms	52080	27227	24853
Cusp forms	48721	26323	22398
Eisenstein series	3359	904	2455

Trace form

26323 * q - 66 * q^2 - 8 * q^3 - 58 * q^4 - 162 * q^5 - 90 * q^6 + 6 * q^7 - 42 * q^8 - 120 * q^9 - 64 * q^10 - 6 * q^11 - 52 * q^12 - 148 * q^13 - 136 * q^14 + 4 * q^15 - 122 * q^16 - 99 * q^17 - 64 * q^18 + 28 * q^19 - 84 * q^20 - 134 * q^21 - 28 * q^22 + 76 * q^23 - 30 * q^24 - 78 * q^25 - 180 * q^26 + 112 * q^27 - 28 * q^28 - 49 * q^29 - 76 * q^30 + 22 * q^31 + 4 * q^32 - 70 * q^33 - 34 * q^34 + 16 * q^35 - 106 * q^36 - 185 * q^37 - 112 * q^38 - 68 * q^39 - 280 * q^40 - 251 * q^41 - 276 * q^42 - 118 * q^43 - 228 * q^44 - 302 * q^45 - 270 * q^46 - 110 * q^47 - 366 * q^48 - 196 * q^49 - 284 * q^50 + 24 * q^51 - 220 * q^52 - 194 * q^53 - 360 * q^54 - 8 * q^55 - 264 * q^56 + 42 * q^57 - 214 * q^58 + 126 * q^59 - 276 * q^60 + 53 * q^61 - 170 * q^62 + 362 * q^63 - 160 * q^64 - 31 * q^65 - 276 * q^66 + 284 * q^67 - 28 * q^68 + 306 * q^69 - 76 * q^70 + 164 * q^71 + 32 * q^72 + 56 * q^73 + 6 * q^74 + 276 * q^75 - 66 * q^76 + 212 * q^77 + 16 * q^78 + 196 * q^79 - 44 * q^80 - 218 * q^81 + 146 * q^82 + 166 * q^83 + 144 * q^84 - 246 * q^85 + 84 * q^86 - 16 * q^87 + 224 * q^88 - 310 * q^89 + 236 * q^90 - 14 * q^91 + 88 * q^92 - 318 * q^93 + 250 * q^94 - 72 * q^95 + 20 * q^96 - 500 * q^97 + 226 * q^98 - 174 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1300))\)

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
1300.2.a	\(\chi_{1300}(1, \cdot)\)	1300.2.a.a	1	1
		1300.2.a.b	1
		1300.2.a.c	1
		1300.2.a.d	1
		1300.2.a.e	1
		1300.2.a.f	1
		1300.2.a.g	2
		1300.2.a.h	2
		1300.2.a.i	3
		1300.2.a.j	3
		1300.2.a.k	3
1300.2.c	\(\chi_{1300}(1249, \cdot)\)	1300.2.c.a	2	1
		1300.2.c.b	2
		1300.2.c.c	2
		1300.2.c.d	2
		1300.2.c.e	4
		1300.2.c.f	6
1300.2.d	\(\chi_{1300}(649, \cdot)\)	1300.2.d.a	4	1
		1300.2.d.b	4
		1300.2.d.c	6
		1300.2.d.d	6
1300.2.f	\(\chi_{1300}(701, \cdot)\)	1300.2.f.a	2	1
		1300.2.f.b	2
		1300.2.f.c	2
		1300.2.f.d	2
		1300.2.f.e	6
		1300.2.f.f	8
1300.2.i	\(\chi_{1300}(601, \cdot)\)	1300.2.i.a	2	2
		1300.2.i.b	2
		1300.2.i.c	2
		1300.2.i.d	2
		1300.2.i.e	2
		1300.2.i.f	2
		1300.2.i.g	10
		1300.2.i.h	10
		1300.2.i.i	12
1300.2.j	\(\chi_{1300}(151, \cdot)\)	n/a	254	2
1300.2.m	\(\chi_{1300}(57, \cdot)\)	1300.2.m.a	2	2
		1300.2.m.b	4
		1300.2.m.c	8
		1300.2.m.d	8
		1300.2.m.e	8
		1300.2.m.f	12
1300.2.o	\(\chi_{1300}(443, \cdot)\)	n/a	216	2
1300.2.p	\(\chi_{1300}(207, \cdot)\)	n/a	244	2
1300.2.r	\(\chi_{1300}(957, \cdot)\)	1300.2.r.a	2	2
		1300.2.r.b	4
		1300.2.r.c	8
		1300.2.r.d	8
		1300.2.r.e	8
		1300.2.r.f	12
1300.2.u	\(\chi_{1300}(99, \cdot)\)	n/a	244	2
1300.2.v	\(\chi_{1300}(261, \cdot)\)	n/a	120	4
1300.2.y	\(\chi_{1300}(101, \cdot)\)	1300.2.y.a	2	2
		1300.2.y.b	8
		1300.2.y.c	10
		1300.2.y.d	10
		1300.2.y.e	16
1300.2.ba	\(\chi_{1300}(49, \cdot)\)	1300.2.ba.a	4	2
		1300.2.ba.b	8
		1300.2.ba.c	8
		1300.2.ba.d	20
1300.2.bb	\(\chi_{1300}(549, \cdot)\)	1300.2.bb.a	4	2
		1300.2.bb.b	4
		1300.2.bb.c	4
		1300.2.bb.d	4
		1300.2.bb.e	4
		1300.2.bb.f	4
		1300.2.bb.g	20
1300.2.be	\(\chi_{1300}(181, \cdot)\)	n/a	136	4
1300.2.bg	\(\chi_{1300}(209, \cdot)\)	n/a	120	4
1300.2.bj	\(\chi_{1300}(129, \cdot)\)	n/a	144	4
1300.2.bk	\(\chi_{1300}(799, \cdot)\)	n/a	488	4
1300.2.bn	\(\chi_{1300}(93, \cdot)\)	1300.2.bn.a	4	4
		1300.2.bn.b	4
		1300.2.bn.c	16
		1300.2.bn.d	20
		1300.2.bn.e	40
1300.2.bo	\(\chi_{1300}(43, \cdot)\)	n/a	488	4
1300.2.br	\(\chi_{1300}(107, \cdot)\)	n/a	488	4
1300.2.bs	\(\chi_{1300}(193, \cdot)\)	1300.2.bs.a	4	4
		1300.2.bs.b	4
		1300.2.bs.c	16
		1300.2.bs.d	20
		1300.2.bs.e	40
1300.2.bv	\(\chi_{1300}(851, \cdot)\)	n/a	508	4
1300.2.bw	\(\chi_{1300}(61, \cdot)\)	n/a	288	8
1300.2.bx	\(\chi_{1300}(239, \cdot)\)	n/a	1648	8
1300.2.bz	\(\chi_{1300}(73, \cdot)\)	n/a	280	8
1300.2.cc	\(\chi_{1300}(103, \cdot)\)	n/a	1648	8
1300.2.cd	\(\chi_{1300}(27, \cdot)\)	n/a	1440	8
1300.2.cg	\(\chi_{1300}(177, \cdot)\)	n/a	280	8
1300.2.ci	\(\chi_{1300}(31, \cdot)\)	n/a	1648	8
1300.2.cj	\(\chi_{1300}(69, \cdot)\)	n/a	288	8
1300.2.cm	\(\chi_{1300}(9, \cdot)\)	n/a	272	8
1300.2.co	\(\chi_{1300}(121, \cdot)\)	n/a	272	8
1300.2.cq	\(\chi_{1300}(11, \cdot)\)	n/a	3296	16
1300.2.cs	\(\chi_{1300}(37, \cdot)\)	n/a	560	16
1300.2.cu	\(\chi_{1300}(3, \cdot)\)	n/a	3296	16
1300.2.cx	\(\chi_{1300}(23, \cdot)\)	n/a	3296	16
1300.2.cz	\(\chi_{1300}(33, \cdot)\)	n/a	560	16
1300.2.db	\(\chi_{1300}(19, \cdot)\)	n/a	3296	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1300))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1300)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 2}\)