Space of modular forms of level 1425 and weight 2

• Label: 1425.2
• Level: 1425
• Weight: 2
• Dimension: 48794
• Nonzero newspaces: 36
• Sturm bound: 288000
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(288000\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1425))\).

	Total	New	Old
Modular forms	74016	50190	23826
Cusp forms	69985	48794	21191
Eisenstein series	4031	1396	2635

Trace form

48794 * q + 2 * q^2 - 99 * q^3 - 184 * q^4 + 12 * q^5 - 143 * q^6 - 178 * q^7 + 42 * q^8 - 91 * q^9 - 220 * q^10 + 8 * q^11 - 67 * q^12 - 150 * q^13 + 84 * q^14 - 116 * q^15 - 240 * q^16 + 22 * q^17 - 106 * q^18 - 184 * q^19 - 72 * q^20 - 156 * q^21 - 212 * q^22 - 14 * q^23 - 183 * q^24 - 316 * q^25 + 48 * q^26 - 87 * q^27 - 244 * q^28 + 8 * q^29 - 172 * q^30 - 286 * q^31 + 56 * q^32 - 43 * q^33 - 104 * q^34 + 40 * q^35 - 135 * q^36 - 124 * q^37 + 118 * q^38 - 204 * q^39 - 292 * q^40 + 80 * q^41 - 159 * q^42 - 178 * q^43 - 6 * q^44 - 272 * q^45 - 312 * q^46 + 4 * q^47 - 251 * q^48 - 292 * q^49 - 212 * q^50 - 441 * q^51 - 430 * q^52 - 112 * q^53 - 401 * q^54 - 296 * q^55 - 220 * q^57 - 520 * q^58 - 56 * q^59 - 172 * q^60 - 210 * q^61 + 82 * q^62 - 85 * q^63 + 112 * q^64 + 116 * q^65 - 73 * q^66 + 134 * q^67 + 370 * q^68 + 136 * q^69 - 8 * q^70 + 184 * q^71 + 156 * q^73 + 412 * q^74 + 84 * q^75 - 434 * q^76 + 246 * q^77 - 25 * q^78 - 118 * q^79 - 124 * q^80 - 319 * q^81 - 376 * q^82 - 250 * q^83 - 553 * q^84 - 652 * q^85 - 370 * q^86 - 521 * q^87 - 1478 * q^88 - 414 * q^89 - 456 * q^90 - 810 * q^91 - 982 * q^92 - 727 * q^93 - 1676 * q^94 - 272 * q^95 - 1524 * q^96 - 928 * q^97 - 1198 * q^98 - 676 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1425))\)

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
1425.2.a	\(\chi_{1425}(1, \cdot)\)	1425.2.a.a	1	1
		1425.2.a.b	1
		1425.2.a.c	1
		1425.2.a.d	1
		1425.2.a.e	1
		1425.2.a.f	1
		1425.2.a.g	1
		1425.2.a.h	1
		1425.2.a.i	1
		1425.2.a.j	1
		1425.2.a.k	2
		1425.2.a.l	2
		1425.2.a.m	2
		1425.2.a.n	2
		1425.2.a.o	2
		1425.2.a.p	2
		1425.2.a.q	2
		1425.2.a.r	2
		1425.2.a.s	3
		1425.2.a.t	3
		1425.2.a.u	3
		1425.2.a.v	3
		1425.2.a.w	3
		1425.2.a.x	3
		1425.2.a.y	7
		1425.2.a.z	7
1425.2.b	\(\chi_{1425}(1424, \cdot)\)	n/a	116	1
1425.2.c	\(\chi_{1425}(799, \cdot)\)	1425.2.c.a	2	1
		1425.2.c.b	2
		1425.2.c.c	2
		1425.2.c.d	2
		1425.2.c.e	2
		1425.2.c.f	2
		1425.2.c.g	2
		1425.2.c.h	2
		1425.2.c.i	4
		1425.2.c.j	4
		1425.2.c.k	4
		1425.2.c.l	4
		1425.2.c.m	4
		1425.2.c.n	4
		1425.2.c.o	6
		1425.2.c.p	6
1425.2.h	\(\chi_{1425}(626, \cdot)\)	n/a	120	1
1425.2.i	\(\chi_{1425}(676, \cdot)\)	n/a	128	2
1425.2.k	\(\chi_{1425}(818, \cdot)\)	n/a	216	2
1425.2.m	\(\chi_{1425}(493, \cdot)\)	n/a	120	2
1425.2.n	\(\chi_{1425}(286, \cdot)\)	n/a	352	4
1425.2.q	\(\chi_{1425}(1076, \cdot)\)	n/a	240	2
1425.2.r	\(\chi_{1425}(449, \cdot)\)	n/a	232	2
1425.2.s	\(\chi_{1425}(49, \cdot)\)	n/a	120	2
1425.2.v	\(\chi_{1425}(226, \cdot)\)	n/a	378	6
1425.2.y	\(\chi_{1425}(56, \cdot)\)	n/a	784	4
1425.2.z	\(\chi_{1425}(229, \cdot)\)	n/a	368	4
1425.2.ba	\(\chi_{1425}(284, \cdot)\)	n/a	784	4
1425.2.bd	\(\chi_{1425}(68, \cdot)\)	n/a	464	4
1425.2.bf	\(\chi_{1425}(943, \cdot)\)	n/a	240	4
1425.2.bh	\(\chi_{1425}(106, \cdot)\)	n/a	800	8
1425.2.bi	\(\chi_{1425}(326, \cdot)\)	n/a	726	6
1425.2.bn	\(\chi_{1425}(199, \cdot)\)	n/a	360	6
1425.2.bo	\(\chi_{1425}(224, \cdot)\)	n/a	696	6
1425.2.bp	\(\chi_{1425}(37, \cdot)\)	n/a	800	8
1425.2.br	\(\chi_{1425}(77, \cdot)\)	n/a	1440	8
1425.2.bt	\(\chi_{1425}(64, \cdot)\)	n/a	800	8
1425.2.bu	\(\chi_{1425}(164, \cdot)\)	n/a	1568	8
1425.2.bz	\(\chi_{1425}(221, \cdot)\)	n/a	1568	8
1425.2.cb	\(\chi_{1425}(193, \cdot)\)	n/a	720	12
1425.2.cc	\(\chi_{1425}(218, \cdot)\)	n/a	1392	12
1425.2.ce	\(\chi_{1425}(16, \cdot)\)	n/a	2400	24
1425.2.cg	\(\chi_{1425}(88, \cdot)\)	n/a	1600	16
1425.2.ci	\(\chi_{1425}(83, \cdot)\)	n/a	3136	16
1425.2.cl	\(\chi_{1425}(41, \cdot)\)	n/a	4704	24
1425.2.cm	\(\chi_{1425}(14, \cdot)\)	n/a	4704	24
1425.2.cn	\(\chi_{1425}(4, \cdot)\)	n/a	2400	24
1425.2.cr	\(\chi_{1425}(17, \cdot)\)	n/a	9408	48
1425.2.cs	\(\chi_{1425}(13, \cdot)\)	n/a	4800	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1425))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1425)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 2}\)