Space of modular forms of level 234 and weight 3

• Label: 234.3
• Level: 234
• Weight: 3
• Dimension: 786
• Nonzero newspaces: 15
• Newform subspaces: 32
• Sturm bound: 9072
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(9072\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(234))\).

	Total	New	Old
Modular forms	3216	786	2430
Cusp forms	2832	786	2046
Eisenstein series	384	0	384

Trace form

786 * q + 36 * q^5 + 24 * q^6 - 8 * q^7 - 12 * q^8 - 24 * q^9 - 54 * q^10 - 48 * q^11 - 24 * q^12 + 18 * q^13 - 48 * q^14 - 36 * q^15 + 16 * q^16 + 36 * q^17 + 48 * q^18 + 184 * q^19 + 96 * q^20 + 84 * q^21 + 120 * q^22 - 60 * q^23 - 36 * q^25 + 72 * q^28 + 672 * q^29 + 240 * q^30 + 408 * q^31 + 252 * q^33 + 168 * q^34 + 660 * q^35 + 72 * q^36 + 144 * q^38 + 6 * q^39 + 48 * q^40 - 210 * q^41 - 192 * q^42 - 296 * q^43 - 432 * q^44 - 732 * q^45 - 624 * q^46 - 1128 * q^47 - 48 * q^48 - 776 * q^49 - 906 * q^50 - 480 * q^51 - 192 * q^52 - 240 * q^53 - 72 * q^54 - 300 * q^55 - 240 * q^56 - 288 * q^57 - 186 * q^58 - 336 * q^59 + 72 * q^60 - 246 * q^61 - 72 * q^62 + 228 * q^63 + 96 * q^64 + 1296 * q^65 + 144 * q^66 + 1108 * q^67 - 132 * q^68 + 540 * q^69 + 528 * q^70 + 1032 * q^71 + 192 * q^72 + 1312 * q^73 - 66 * q^74 + 264 * q^75 - 128 * q^76 + 180 * q^77 - 144 * q^78 - 36 * q^79 + 48 * q^80 + 120 * q^81 - 354 * q^82 - 576 * q^83 + 288 * q^84 - 1566 * q^85 + 120 * q^86 - 852 * q^87 - 240 * q^88 - 1512 * q^89 - 1304 * q^91 - 24 * q^92 - 1596 * q^93 - 408 * q^94 - 1416 * q^95 - 96 * q^96 + 156 * q^97 - 1104 * q^98 - 2700 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(234))\)

We only show spaces with odd 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
234.3.c	\(\chi_{234}(53, \cdot)\)	234.3.c.a	4	1
		234.3.c.b	4
234.3.d	\(\chi_{234}(233, \cdot)\)	234.3.d.a	4	1
		234.3.d.b	4
		234.3.d.c	4
234.3.i	\(\chi_{234}(73, \cdot)\)	234.3.i.a	2	2
		234.3.i.b	4
		234.3.i.c	6
		234.3.i.d	6
		234.3.i.e	8
234.3.k	\(\chi_{234}(35, \cdot)\)	234.3.k.a	4	2
		234.3.k.b	12
234.3.m	\(\chi_{234}(23, \cdot)\)	234.3.m.a	56	2
234.3.n	\(\chi_{234}(77, \cdot)\)	234.3.n.a	56	2
234.3.o	\(\chi_{234}(95, \cdot)\)	234.3.o.a	56	2
234.3.q	\(\chi_{234}(29, \cdot)\)	234.3.q.a	56	2
234.3.r	\(\chi_{234}(131, \cdot)\)	234.3.r.a	48	2
234.3.u	\(\chi_{234}(185, \cdot)\)	234.3.u.a	56	2
234.3.v	\(\chi_{234}(17, \cdot)\)	234.3.v.a	16	2
234.3.w	\(\chi_{234}(31, \cdot)\)	234.3.w.a	56	4
		234.3.w.b	56
234.3.ba	\(\chi_{234}(7, \cdot)\)	234.3.ba.a	56	4
		234.3.ba.b	56
234.3.bb	\(\chi_{234}(19, \cdot)\)	234.3.bb.a	4	4
		234.3.bb.b	4
		234.3.bb.c	4
		234.3.bb.d	8
		234.3.bb.e	8
		234.3.bb.f	8
		234.3.bb.g	8
234.3.bc	\(\chi_{234}(85, \cdot)\)	234.3.bc.a	56	4
		234.3.bc.b	56

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(234))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(234)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)