Space of modular forms of level 231 and weight 4

• Label: 231.4
• Level: 231
• Weight: 4
• Dimension: 3980
• Nonzero newspaces: 16
• Newform subspaces: 34
• Sturm bound: 15360
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 34 \)
Sturm bound:			\(15360\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(231))\).

	Total	New	Old
Modular forms	6000	4156	1844
Cusp forms	5520	3980	1540
Eisenstein series	480	176	304

Trace form

3980 * q - 26 * q^3 - 28 * q^4 + 48 * q^5 - 48 * q^6 + 38 * q^7 + 52 * q^8 + 62 * q^9 + 244 * q^10 + 200 * q^11 + 472 * q^12 + 208 * q^13 + 234 * q^14 - 274 * q^15 - 1308 * q^16 - 576 * q^17 - 840 * q^18 - 256 * q^19 - 188 * q^20 - 780 * q^21 + 1988 * q^22 + 1096 * q^23 + 1712 * q^24 + 1532 * q^25 + 688 * q^26 + 136 * q^27 + 1120 * q^28 - 104 * q^29 - 830 * q^30 - 1300 * q^31 - 1124 * q^32 - 2829 * q^33 - 3288 * q^34 - 1328 * q^35 - 3006 * q^36 - 2804 * q^37 - 2120 * q^38 - 304 * q^39 + 188 * q^40 + 4056 * q^41 - 2234 * q^42 - 2104 * q^43 - 644 * q^44 + 998 * q^45 + 2124 * q^46 + 776 * q^47 + 6222 * q^48 + 6622 * q^49 + 9376 * q^50 + 8208 * q^51 + 14100 * q^52 + 3560 * q^53 + 9366 * q^54 - 1820 * q^55 - 1740 * q^56 - 1440 * q^57 - 3716 * q^58 + 2712 * q^59 - 6050 * q^60 + 1204 * q^61 + 6936 * q^62 + 819 * q^63 - 1456 * q^64 + 2352 * q^65 - 7032 * q^66 - 6916 * q^67 - 8128 * q^68 - 6338 * q^69 - 10392 * q^70 - 13776 * q^71 - 11870 * q^72 - 13828 * q^73 - 15240 * q^74 - 11022 * q^75 - 26512 * q^76 - 12600 * q^77 - 4208 * q^78 - 4420 * q^79 - 24972 * q^80 - 5794 * q^81 - 536 * q^82 + 920 * q^83 - 11562 * q^84 + 14404 * q^85 + 6628 * q^86 + 12198 * q^87 + 44492 * q^88 + 20104 * q^89 + 12370 * q^90 + 20262 * q^91 + 26668 * q^92 + 6666 * q^93 + 452 * q^94 + 6072 * q^95 - 7550 * q^96 - 12580 * q^97 + 6904 * q^98 - 5344 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(231))\)

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
231.4.a	\(\chi_{231}(1, \cdot)\)	231.4.a.a	1	1
		231.4.a.b	1
		231.4.a.c	1
		231.4.a.d	1
		231.4.a.e	1
		231.4.a.f	2
		231.4.a.g	2
		231.4.a.h	2
		231.4.a.i	2
		231.4.a.j	5
		231.4.a.k	5
		231.4.a.l	5
231.4.c	\(\chi_{231}(76, \cdot)\)	231.4.c.a	48	1
231.4.e	\(\chi_{231}(188, \cdot)\)	231.4.e.a	80	1
231.4.g	\(\chi_{231}(197, \cdot)\)	231.4.g.a	72	1
231.4.i	\(\chi_{231}(67, \cdot)\)	231.4.i.a	16	2
		231.4.i.b	20
		231.4.i.c	20
		231.4.i.d	24
231.4.j	\(\chi_{231}(64, \cdot)\)	231.4.j.a	28	4
		231.4.j.b	36
		231.4.j.c	36
		231.4.j.d	44
231.4.l	\(\chi_{231}(32, \cdot)\)	231.4.l.a	184	2
231.4.n	\(\chi_{231}(89, \cdot)\)	231.4.n.a	160	2
231.4.p	\(\chi_{231}(10, \cdot)\)	231.4.p.a	96	2
231.4.s	\(\chi_{231}(8, \cdot)\)	231.4.s.a	288	4
231.4.u	\(\chi_{231}(20, \cdot)\)	231.4.u.a	368	4
231.4.w	\(\chi_{231}(13, \cdot)\)	231.4.w.a	192	4
231.4.y	\(\chi_{231}(4, \cdot)\)	231.4.y.a	192	8
		231.4.y.b	192
231.4.ba	\(\chi_{231}(19, \cdot)\)	231.4.ba.a	384	8
231.4.bc	\(\chi_{231}(5, \cdot)\)	231.4.bc.a	736	8
231.4.be	\(\chi_{231}(2, \cdot)\)	231.4.be.a	736	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(231))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(231)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)