Space of modular forms of level 3025 and weight 2

• Label: 3025.2
• Level: 3025
• Weight: 2
• Dimension: 326177
• Nonzero newspaces: 42
• Sturm bound: 1452000
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 42 \)
Sturm bound:			\(1452000\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3025))\).

	Total	New	Old
Modular forms	367480	331938	35542
Cusp forms	358521	326177	32344
Eisenstein series	8959	5761	3198

Trace form

326177 * q - 592 * q^2 - 591 * q^3 - 588 * q^4 - 725 * q^5 - 941 * q^6 - 577 * q^7 - 560 * q^8 - 562 * q^9 - 715 * q^10 - 1045 * q^11 - 1047 * q^12 - 571 * q^13 - 541 * q^14 - 710 * q^15 - 888 * q^16 - 557 * q^17 - 521 * q^18 - 565 * q^19 - 730 * q^20 - 901 * q^21 - 620 * q^22 - 1081 * q^23 - 495 * q^24 - 735 * q^25 - 1761 * q^26 - 525 * q^27 - 489 * q^28 - 535 * q^29 - 710 * q^30 - 911 * q^31 - 467 * q^32 - 610 * q^33 - 1006 * q^34 - 700 * q^35 - 748 * q^36 - 502 * q^37 - 455 * q^38 - 469 * q^39 - 865 * q^40 - 851 * q^41 - 569 * q^42 - 661 * q^43 - 740 * q^44 - 1505 * q^45 - 1141 * q^46 - 757 * q^47 - 1031 * q^48 - 883 * q^49 - 905 * q^50 - 2051 * q^51 - 1077 * q^52 - 716 * q^53 - 1075 * q^54 - 880 * q^55 - 2195 * q^56 - 765 * q^57 - 1045 * q^58 - 725 * q^59 - 1050 * q^60 - 1171 * q^61 - 719 * q^62 - 791 * q^63 - 958 * q^64 - 835 * q^65 - 1085 * q^66 - 1197 * q^67 - 659 * q^68 - 549 * q^69 - 770 * q^70 - 791 * q^71 - 670 * q^72 - 431 * q^73 - 361 * q^74 - 710 * q^75 - 1575 * q^76 - 565 * q^77 - 777 * q^78 - 385 * q^79 - 715 * q^80 - 688 * q^81 - 379 * q^82 - 451 * q^83 - 461 * q^84 - 755 * q^85 - 721 * q^86 - 375 * q^87 - 490 * q^88 - 1020 * q^89 - 1105 * q^90 - 881 * q^91 - 637 * q^92 - 817 * q^93 - 861 * q^94 - 870 * q^95 - 1541 * q^96 - 917 * q^97 - 1144 * q^98 - 910 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3025))\)

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
3025.2.a	\(\chi_{3025}(1, \cdot)\)	3025.2.a.a	1	1
		3025.2.a.b	1
		3025.2.a.c	1
		3025.2.a.d	1
		3025.2.a.e	1
		3025.2.a.f	1
		3025.2.a.g	1
		3025.2.a.h	2
		3025.2.a.i	2
		3025.2.a.j	2
		3025.2.a.k	2
		3025.2.a.l	2
		3025.2.a.m	2
		3025.2.a.n	2
		3025.2.a.o	2
		3025.2.a.p	3
		3025.2.a.q	3
		3025.2.a.r	3
		3025.2.a.s	3
		3025.2.a.t	3
		3025.2.a.u	3
		3025.2.a.v	4
		3025.2.a.w	4
		3025.2.a.x	4
		3025.2.a.y	4
		3025.2.a.z	4
		3025.2.a.ba	4
		3025.2.a.bb	4
		3025.2.a.bc	4
		3025.2.a.bd	4
		3025.2.a.be	4
		3025.2.a.bf	6
		3025.2.a.bg	6
		3025.2.a.bh	6
		3025.2.a.bi	8
		3025.2.a.bj	8
		3025.2.a.bk	8
		3025.2.a.bl	8
		3025.2.a.bm	8
		3025.2.a.bn	8
		3025.2.a.bo	12
3025.2.b	\(\chi_{3025}(1574, \cdot)\)	n/a	154	1
3025.2.e	\(\chi_{3025}(1693, \cdot)\)	n/a	308	2
3025.2.g	\(\chi_{3025}(1116, \cdot)\)	n/a	1048	4
3025.2.h	\(\chi_{3025}(251, \cdot)\)	n/a	636	4
3025.2.i	\(\chi_{3025}(606, \cdot)\)	n/a	1052	4
3025.2.j	\(\chi_{3025}(81, \cdot)\)	n/a	1048	4
3025.2.k	\(\chi_{3025}(1291, \cdot)\)	n/a	1048	4
3025.2.l	\(\chi_{3025}(366, \cdot)\)	n/a	1048	4
3025.2.n	\(\chi_{3025}(1219, \cdot)\)	n/a	1048	4
3025.2.t	\(\chi_{3025}(269, \cdot)\)	n/a	1048	4
3025.2.y	\(\chi_{3025}(364, \cdot)\)	n/a	1056	4
3025.2.z	\(\chi_{3025}(124, \cdot)\)	n/a	616	4
3025.2.ba	\(\chi_{3025}(614, \cdot)\)	n/a	1048	4
3025.2.bb	\(\chi_{3025}(9, \cdot)\)	n/a	1048	4
3025.2.be	\(\chi_{3025}(276, \cdot)\)	n/a	2060	10
3025.2.bg	\(\chi_{3025}(233, \cdot)\)	n/a	2096	8
3025.2.bh	\(\chi_{3025}(112, \cdot)\)	n/a	2096	8
3025.2.bm	\(\chi_{3025}(602, \cdot)\)	n/a	2096	8
3025.2.bn	\(\chi_{3025}(118, \cdot)\)	n/a	1232	8
3025.2.bo	\(\chi_{3025}(403, \cdot)\)	n/a	2096	8
3025.2.bp	\(\chi_{3025}(362, \cdot)\)	n/a	2096	8
3025.2.bs	\(\chi_{3025}(199, \cdot)\)	n/a	1960	10
3025.2.bv	\(\chi_{3025}(32, \cdot)\)	n/a	3920	20
3025.2.bw	\(\chi_{3025}(31, \cdot)\)	n/a	13120	40
3025.2.bx	\(\chi_{3025}(141, \cdot)\)	n/a	13120	40
3025.2.by	\(\chi_{3025}(56, \cdot)\)	n/a	13120	40
3025.2.bz	\(\chi_{3025}(26, \cdot)\)	n/a	8240	40
3025.2.ca	\(\chi_{3025}(16, \cdot)\)	n/a	13120	40
3025.2.cb	\(\chi_{3025}(36, \cdot)\)	n/a	13120	40
3025.2.cd	\(\chi_{3025}(14, \cdot)\)	n/a	13120	40
3025.2.ci	\(\chi_{3025}(169, \cdot)\)	n/a	13120	40
3025.2.cj	\(\chi_{3025}(4, \cdot)\)	n/a	13120	40
3025.2.ck	\(\chi_{3025}(49, \cdot)\)	n/a	7840	40
3025.2.cl	\(\chi_{3025}(34, \cdot)\)	n/a	13120	40
3025.2.ct	\(\chi_{3025}(104, \cdot)\)	n/a	13120	40
3025.2.cv	\(\chi_{3025}(17, \cdot)\)	n/a	26240	80
3025.2.cw	\(\chi_{3025}(87, \cdot)\)	n/a	26240	80
3025.2.cx	\(\chi_{3025}(2, \cdot)\)	n/a	26240	80
3025.2.cy	\(\chi_{3025}(7, \cdot)\)	n/a	15680	80
3025.2.dd	\(\chi_{3025}(13, \cdot)\)	n/a	26240	80
3025.2.de	\(\chi_{3025}(28, \cdot)\)	n/a	26240	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 2}\)