Space of modular forms of level 3234 and weight 2

• Label: 3234.2
• Level: 3234
• Weight: 2
• Dimension: 66584
• Nonzero newspaces: 32
• Sturm bound: 1128960
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(1128960\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3234))\).

	Total	New	Old
Modular forms	287040	66584	220456
Cusp forms	277441	66584	210857
Eisenstein series	9599	0	9599

Trace form

66584 * q + 2 * q^2 - 6 * q^3 - 14 * q^4 - 36 * q^5 - 27 * q^6 - 32 * q^7 + 2 * q^8 - 50 * q^9 - 56 * q^10 - 56 * q^11 - 16 * q^12 - 56 * q^13 - 18 * q^15 + 2 * q^16 - 52 * q^17 + 45 * q^18 - 54 * q^19 + 12 * q^20 + 20 * q^21 + 12 * q^22 - 20 * q^23 + 31 * q^24 - 74 * q^25 - 20 * q^26 + 24 * q^27 - 24 * q^28 - 56 * q^29 - 6 * q^30 - 116 * q^31 + 2 * q^32 + 9 * q^33 - 60 * q^34 - 96 * q^35 - 25 * q^36 + 76 * q^37 + 64 * q^38 + 122 * q^39 + 132 * q^40 + 208 * q^41 + 108 * q^42 + 44 * q^43 + 28 * q^44 + 132 * q^45 + 320 * q^46 + 208 * q^47 + 22 * q^48 + 576 * q^49 + 166 * q^50 + 365 * q^51 + 76 * q^52 + 240 * q^53 + 64 * q^54 + 320 * q^55 + 144 * q^56 + 91 * q^57 + 364 * q^58 + 204 * q^59 + 124 * q^60 + 496 * q^61 + 316 * q^62 + 240 * q^63 - 14 * q^64 + 432 * q^65 + 432 * q^66 + 420 * q^67 + 188 * q^68 + 522 * q^69 + 360 * q^70 + 736 * q^71 + 174 * q^72 + 580 * q^73 + 372 * q^74 + 825 * q^75 + 196 * q^76 + 252 * q^77 + 372 * q^78 + 340 * q^79 + 184 * q^80 + 866 * q^81 + 266 * q^82 + 684 * q^83 + 68 * q^84 + 684 * q^85 + 508 * q^86 + 756 * q^87 + 208 * q^88 + 552 * q^89 + 454 * q^90 + 472 * q^91 - 48 * q^92 + 786 * q^93 + 88 * q^94 + 660 * q^95 + 26 * q^96 + 102 * q^97 - 48 * q^98 + 210 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3234))\)

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
3234.2.a	\(\chi_{3234}(1, \cdot)\)	3234.2.a.a	1	1
		3234.2.a.b	1
		3234.2.a.c	1
		3234.2.a.d	1
		3234.2.a.e	1
		3234.2.a.f	1
		3234.2.a.g	1
		3234.2.a.h	1
		3234.2.a.i	1
		3234.2.a.j	1
		3234.2.a.k	1
		3234.2.a.l	1
		3234.2.a.m	1
		3234.2.a.n	1
		3234.2.a.o	1
		3234.2.a.p	1
		3234.2.a.q	1
		3234.2.a.r	1
		3234.2.a.s	1
		3234.2.a.t	1
		3234.2.a.u	1
		3234.2.a.v	1
		3234.2.a.w	2
		3234.2.a.x	2
		3234.2.a.y	2
		3234.2.a.z	2
		3234.2.a.ba	2
		3234.2.a.bb	2
		3234.2.a.bc	2
		3234.2.a.bd	2
		3234.2.a.be	2
		3234.2.a.bf	3
		3234.2.a.bg	3
		3234.2.a.bh	3
		3234.2.a.bi	3
		3234.2.a.bj	4
		3234.2.a.bk	4
		3234.2.a.bl	4
		3234.2.a.bm	4
3234.2.c	\(\chi_{3234}(197, \cdot)\)	n/a	164	1
3234.2.e	\(\chi_{3234}(2155, \cdot)\)	3234.2.e.a	16	1
		3234.2.e.b	16
		3234.2.e.c	24
		3234.2.e.d	24
3234.2.g	\(\chi_{3234}(881, \cdot)\)	n/a	136	1
3234.2.i	\(\chi_{3234}(67, \cdot)\)	n/a	136	2
3234.2.j	\(\chi_{3234}(295, \cdot)\)	n/a	328	4
3234.2.k	\(\chi_{3234}(815, \cdot)\)	n/a	264	2
3234.2.n	\(\chi_{3234}(263, \cdot)\)	n/a	320	2
3234.2.p	\(\chi_{3234}(901, \cdot)\)	n/a	160	2
3234.2.r	\(\chi_{3234}(463, \cdot)\)	n/a	576	6
3234.2.t	\(\chi_{3234}(587, \cdot)\)	n/a	640	4
3234.2.v	\(\chi_{3234}(391, \cdot)\)	n/a	320	4
3234.2.x	\(\chi_{3234}(491, \cdot)\)	n/a	656	4
3234.2.ba	\(\chi_{3234}(419, \cdot)\)	n/a	1104	6
3234.2.bc	\(\chi_{3234}(307, \cdot)\)	n/a	672	6
3234.2.be	\(\chi_{3234}(659, \cdot)\)	n/a	1344	6
3234.2.bg	\(\chi_{3234}(361, \cdot)\)	n/a	640	8
3234.2.bh	\(\chi_{3234}(331, \cdot)\)	n/a	1104	12
3234.2.bj	\(\chi_{3234}(19, \cdot)\)	n/a	640	8
3234.2.bl	\(\chi_{3234}(557, \cdot)\)	n/a	1280	8
3234.2.bo	\(\chi_{3234}(509, \cdot)\)	n/a	1280	8
3234.2.bp	\(\chi_{3234}(169, \cdot)\)	n/a	2688	24
3234.2.br	\(\chi_{3234}(241, \cdot)\)	n/a	1344	12
3234.2.bt	\(\chi_{3234}(65, \cdot)\)	n/a	2688	12
3234.2.bw	\(\chi_{3234}(89, \cdot)\)	n/a	2256	12
3234.2.by	\(\chi_{3234}(29, \cdot)\)	n/a	5376	24
3234.2.ca	\(\chi_{3234}(13, \cdot)\)	n/a	2688	24
3234.2.cc	\(\chi_{3234}(125, \cdot)\)	n/a	5376	24
3234.2.ce	\(\chi_{3234}(25, \cdot)\)	n/a	5376	48
3234.2.cf	\(\chi_{3234}(5, \cdot)\)	n/a	10752	48
3234.2.ci	\(\chi_{3234}(95, \cdot)\)	n/a	10752	48
3234.2.ck	\(\chi_{3234}(61, \cdot)\)	n/a	5376	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3234))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3234)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1078))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1617))\)\(^{\oplus 2}\)