Space of modular forms of level 1225 and weight 2

• Label: 1225.2
• Level: 1225
• Weight: 2
• Dimension: 51010
• Nonzero newspaces: 24
• Sturm bound: 235200
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(235200\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1225))\).

	Total	New	Old
Modular forms	60480	52999	7481
Cusp forms	57121	51010	6111
Eisenstein series	3359	1989	1370

Trace form

51010 * q - 202 * q^2 - 199 * q^3 - 190 * q^4 - 245 * q^5 - 303 * q^6 - 230 * q^7 - 328 * q^8 - 172 * q^9 - 235 * q^10 - 303 * q^11 - 127 * q^12 - 169 * q^13 - 216 * q^14 - 422 * q^15 - 262 * q^16 - 167 * q^17 - 119 * q^18 - 171 * q^19 - 250 * q^20 - 353 * q^21 - 305 * q^22 - 159 * q^23 - 293 * q^24 - 279 * q^25 - 639 * q^26 - 265 * q^27 - 284 * q^28 - 399 * q^29 - 374 * q^30 - 359 * q^31 - 345 * q^32 - 327 * q^33 - 314 * q^34 - 324 * q^35 - 818 * q^36 - 274 * q^37 - 295 * q^38 - 372 * q^39 - 369 * q^40 - 371 * q^41 - 381 * q^42 - 419 * q^43 - 347 * q^44 - 337 * q^45 - 405 * q^46 - 197 * q^47 - 452 * q^48 - 272 * q^49 - 793 * q^50 - 577 * q^51 - 373 * q^52 - 136 * q^53 - 395 * q^54 - 278 * q^55 - 498 * q^56 - 447 * q^57 - 479 * q^58 - 315 * q^59 - 490 * q^60 - 530 * q^61 - 507 * q^62 - 366 * q^63 - 750 * q^64 - 379 * q^65 - 591 * q^66 - 431 * q^67 - 577 * q^68 - 425 * q^69 - 468 * q^70 - 613 * q^71 - 612 * q^72 - 413 * q^73 - 507 * q^74 - 422 * q^75 - 917 * q^76 - 297 * q^77 - 683 * q^78 - 395 * q^79 - 547 * q^80 - 424 * q^81 - 538 * q^82 - 345 * q^83 - 608 * q^84 - 563 * q^85 - 498 * q^86 - 389 * q^87 - 774 * q^88 - 390 * q^89 - 601 * q^90 - 463 * q^91 - 732 * q^92 - 545 * q^93 - 512 * q^94 - 422 * q^95 - 874 * q^96 - 450 * q^97 - 672 * q^98 - 860 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1225))\)

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
1225.2.a	\(\chi_{1225}(1, \cdot)\)	1225.2.a.a	1	1
		1225.2.a.b	1
		1225.2.a.c	1
		1225.2.a.d	1
		1225.2.a.e	1
		1225.2.a.f	1
		1225.2.a.g	1
		1225.2.a.h	1
		1225.2.a.i	1
		1225.2.a.j	1
		1225.2.a.k	2
		1225.2.a.l	2
		1225.2.a.m	2
		1225.2.a.n	2
		1225.2.a.o	2
		1225.2.a.p	2
		1225.2.a.q	2
		1225.2.a.r	2
		1225.2.a.s	2
		1225.2.a.t	2
		1225.2.a.u	2
		1225.2.a.v	2
		1225.2.a.w	3
		1225.2.a.x	3
		1225.2.a.y	3
		1225.2.a.z	3
		1225.2.a.ba	4
		1225.2.a.bb	4
		1225.2.a.bc	4
1225.2.b	\(\chi_{1225}(99, \cdot)\)	1225.2.b.a	2	1
		1225.2.b.b	2
		1225.2.b.c	2
		1225.2.b.d	2
		1225.2.b.e	4
		1225.2.b.f	4
		1225.2.b.g	4
		1225.2.b.h	4
		1225.2.b.i	4
		1225.2.b.j	4
		1225.2.b.k	4
		1225.2.b.l	6
		1225.2.b.m	6
		1225.2.b.n	8
1225.2.e	\(\chi_{1225}(226, \cdot)\)	n/a	114	2
1225.2.f	\(\chi_{1225}(293, \cdot)\)	n/a	112	2
1225.2.h	\(\chi_{1225}(246, \cdot)\)	n/a	388	4
1225.2.k	\(\chi_{1225}(324, \cdot)\)	n/a	112	2
1225.2.l	\(\chi_{1225}(176, \cdot)\)	n/a	510	6
1225.2.o	\(\chi_{1225}(344, \cdot)\)	n/a	392	4
1225.2.p	\(\chi_{1225}(68, \cdot)\)	n/a	224	4
1225.2.t	\(\chi_{1225}(274, \cdot)\)	n/a	492	6
1225.2.u	\(\chi_{1225}(116, \cdot)\)	n/a	768	8
1225.2.w	\(\chi_{1225}(48, \cdot)\)	n/a	768	8
1225.2.x	\(\chi_{1225}(51, \cdot)\)	n/a	1032	12
1225.2.z	\(\chi_{1225}(118, \cdot)\)	n/a	984	12
1225.2.ba	\(\chi_{1225}(79, \cdot)\)	n/a	768	8
1225.2.bd	\(\chi_{1225}(36, \cdot)\)	n/a	3312	24
1225.2.be	\(\chi_{1225}(74, \cdot)\)	n/a	984	12
1225.2.bi	\(\chi_{1225}(117, \cdot)\)	n/a	1536	16
1225.2.bj	\(\chi_{1225}(29, \cdot)\)	n/a	3312	24
1225.2.bn	\(\chi_{1225}(82, \cdot)\)	n/a	1968	24
1225.2.bo	\(\chi_{1225}(11, \cdot)\)	n/a	6624	48
1225.2.bp	\(\chi_{1225}(13, \cdot)\)	n/a	6624	48
1225.2.bt	\(\chi_{1225}(4, \cdot)\)	n/a	6624	48
1225.2.bu	\(\chi_{1225}(3, \cdot)\)	n/a	13248	96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1225))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 1}\)