Space of modular forms of level 3267 and weight 2

• Label: 3267.2
• Level: 3267
• Weight: 2
• Dimension: 302413
• Nonzero newspaces: 24
• Sturm bound: 1568160
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 3267 = 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(1568160\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3267))\).

	Total	New	Old
Modular forms	396840	306909	89931
Cusp forms	387241	302413	84828
Eisenstein series	9599	4496	5103

Trace form

302413 * q - 366 * q^2 - 546 * q^3 - 638 * q^4 - 363 * q^5 - 540 * q^6 - 637 * q^7 - 354 * q^8 - 540 * q^9 - 633 * q^10 - 400 * q^11 - 1008 * q^12 - 631 * q^13 - 345 * q^14 - 531 * q^15 - 626 * q^16 - 351 * q^17 - 531 * q^18 - 640 * q^19 - 323 * q^20 - 552 * q^21 - 700 * q^22 - 672 * q^23 - 558 * q^24 - 592 * q^25 - 310 * q^26 - 549 * q^27 - 1330 * q^28 - 306 * q^29 - 549 * q^30 - 591 * q^31 - 200 * q^32 - 600 * q^33 - 1101 * q^34 - 248 * q^35 - 522 * q^36 - 582 * q^37 - 198 * q^38 - 507 * q^39 - 489 * q^40 - 285 * q^41 - 522 * q^42 - 579 * q^43 - 370 * q^44 - 1029 * q^45 - 633 * q^46 - 375 * q^47 - 555 * q^48 - 624 * q^49 - 293 * q^50 - 558 * q^51 - 551 * q^52 - 298 * q^53 - 594 * q^54 - 1560 * q^55 - 513 * q^56 - 543 * q^57 - 449 * q^58 - 232 * q^59 - 540 * q^60 - 539 * q^61 - 72 * q^62 - 531 * q^63 - 466 * q^64 - 177 * q^65 - 600 * q^66 - 1040 * q^67 - 51 * q^68 - 531 * q^69 - 405 * q^70 - 173 * q^71 - 522 * q^72 - 551 * q^73 - 47 * q^74 - 501 * q^75 - 504 * q^76 - 320 * q^77 - 1002 * q^78 - 575 * q^79 - 958 * q^80 - 624 * q^81 - 1492 * q^82 - 601 * q^83 - 1014 * q^84 - 977 * q^85 - 969 * q^86 - 831 * q^87 - 1020 * q^88 - 1171 * q^89 - 1122 * q^90 - 869 * q^91 - 1519 * q^92 - 879 * q^93 - 1285 * q^94 - 1193 * q^95 - 1500 * q^96 - 966 * q^97 - 1405 * q^98 - 840 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3267))\)

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
3267.2.a	\(\chi_{3267}(1, \cdot)\)	3267.2.a.a	1	1
		3267.2.a.b	1
		3267.2.a.c	1
		3267.2.a.d	1
		3267.2.a.e	1
		3267.2.a.f	1
		3267.2.a.g	1
		3267.2.a.h	1
		3267.2.a.i	1
		3267.2.a.j	1
		3267.2.a.k	1
		3267.2.a.l	2
		3267.2.a.m	2
		3267.2.a.n	2
		3267.2.a.o	2
		3267.2.a.p	2
		3267.2.a.q	2
		3267.2.a.r	3
		3267.2.a.s	3
		3267.2.a.t	3
		3267.2.a.u	3
		3267.2.a.v	3
		3267.2.a.w	3
		3267.2.a.x	4
		3267.2.a.y	4
		3267.2.a.z	4
		3267.2.a.ba	4
		3267.2.a.bb	4
		3267.2.a.bc	6
		3267.2.a.bd	6
		3267.2.a.be	8
		3267.2.a.bf	8
		3267.2.a.bg	8
		3267.2.a.bh	8
		3267.2.a.bi	8
		3267.2.a.bj	8
		3267.2.a.bk	8
		3267.2.a.bl	8
		3267.2.a.bm	8
3267.2.d	\(\chi_{3267}(3266, \cdot)\)	n/a	144	1
3267.2.e	\(\chi_{3267}(1090, \cdot)\)	n/a	200	2
3267.2.f	\(\chi_{3267}(487, \cdot)\)	n/a	576	4
3267.2.g	\(\chi_{3267}(1088, \cdot)\)	n/a	200	2
3267.2.j	\(\chi_{3267}(364, \cdot)\)	n/a	1908	6
3267.2.k	\(\chi_{3267}(161, \cdot)\)	n/a	576	4
3267.2.n	\(\chi_{3267}(298, \cdot)\)	n/a	1760	10
3267.2.o	\(\chi_{3267}(856, \cdot)\)	n/a	800	8
3267.2.p	\(\chi_{3267}(362, \cdot)\)	n/a	1896	6
3267.2.s	\(\chi_{3267}(296, \cdot)\)	n/a	1760	10
3267.2.x	\(\chi_{3267}(233, \cdot)\)	n/a	800	8
3267.2.y	\(\chi_{3267}(100, \cdot)\)	n/a	2600	20
3267.2.z	\(\chi_{3267}(124, \cdot)\)	n/a	7584	24
3267.2.ba	\(\chi_{3267}(82, \cdot)\)	n/a	7040	40
3267.2.bd	\(\chi_{3267}(98, \cdot)\)	n/a	2600	20
3267.2.bg	\(\chi_{3267}(239, \cdot)\)	n/a	7584	24
3267.2.bh	\(\chi_{3267}(34, \cdot)\)	n/a	23640	60
3267.2.bk	\(\chi_{3267}(107, \cdot)\)	n/a	7040	40
3267.2.bl	\(\chi_{3267}(37, \cdot)\)	n/a	10400	80
3267.2.bo	\(\chi_{3267}(32, \cdot)\)	n/a	23640	60
3267.2.bp	\(\chi_{3267}(8, \cdot)\)	n/a	10400	80
3267.2.bs	\(\chi_{3267}(4, \cdot)\)	n/a	94560	240
3267.2.bt	\(\chi_{3267}(2, \cdot)\)	n/a	94560	240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3267))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3267)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3267))\)\(^{\oplus 1}\)