Space of modular forms of level 230 and weight 4

• Label: 230.4
• Level: 230
• Weight: 4
• Dimension: 1446
• Nonzero newspaces: 6
• Newform subspaces: 19
• Sturm bound: 12672
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(12672\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(230))\).

	Total	New	Old
Modular forms	4928	1446	3482
Cusp forms	4576	1446	3130
Eisenstein series	352	0	352

Trace form

1446 * q - 4 * q^2 + 16 * q^3 + 8 * q^4 + 10 * q^5 + 16 * q^6 + 8 * q^7 - 16 * q^8 - 166 * q^9 - 100 * q^10 + 88 * q^11 + 64 * q^12 + 116 * q^13 + 224 * q^14 - 588 * q^15 - 96 * q^16 - 484 * q^17 + 28 * q^18 + 400 * q^19 + 232 * q^20 + 2368 * q^21 + 920 * q^22 + 1804 * q^23 + 192 * q^24 + 954 * q^25 + 576 * q^26 + 424 * q^27 - 320 * q^28 - 340 * q^29 - 1256 * q^30 - 1992 * q^31 - 64 * q^32 - 3680 * q^33 - 776 * q^34 - 2430 * q^35 + 72 * q^36 - 2308 * q^37 + 400 * q^38 - 568 * q^39 + 240 * q^40 + 1008 * q^41 - 128 * q^42 + 3368 * q^43 - 544 * q^44 + 3060 * q^45 - 32 * q^46 + 4192 * q^47 + 256 * q^48 + 6342 * q^49 + 700 * q^50 + 2888 * q^51 + 464 * q^52 - 928 * q^53 - 6728 * q^54 - 7676 * q^55 - 4640 * q^56 - 17704 * q^57 - 3336 * q^58 - 10820 * q^59 - 88 * q^60 - 1860 * q^61 + 2824 * q^62 + 8656 * q^63 + 128 * q^64 + 9684 * q^65 + 11744 * q^66 + 7856 * q^67 + 5456 * q^68 + 15784 * q^69 + 4848 * q^70 + 17288 * q^71 + 4336 * q^72 + 3500 * q^73 + 8712 * q^74 - 378 * q^75 + 1760 * q^76 - 784 * q^77 - 4760 * q^78 - 12812 * q^79 - 1248 * q^80 - 18126 * q^81 - 8280 * q^82 - 18052 * q^83 - 6992 * q^84 - 5998 * q^85 - 13496 * q^86 + 7932 * q^87 - 192 * q^88 + 160 * q^89 - 2580 * q^90 + 6296 * q^91 - 528 * q^92 + 2432 * q^93 + 2624 * q^94 + 23232 * q^95 + 256 * q^96 + 25816 * q^97 + 15212 * q^98 + 34028 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(230))\)

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
230.4.a	\(\chi_{230}(1, \cdot)\)	230.4.a.a	1	1
		230.4.a.b	1
		230.4.a.c	1
		230.4.a.d	1
		230.4.a.e	1
		230.4.a.f	2
		230.4.a.g	3
		230.4.a.h	4
		230.4.a.i	4
		230.4.a.j	4
230.4.b	\(\chi_{230}(139, \cdot)\)	230.4.b.a	14	1
		230.4.b.b	18
230.4.e	\(\chi_{230}(137, \cdot)\)	230.4.e.a	72	2
230.4.g	\(\chi_{230}(31, \cdot)\)	230.4.g.a	50	10
		230.4.g.b	60
		230.4.g.c	60
		230.4.g.d	70
230.4.j	\(\chi_{230}(9, \cdot)\)	230.4.j.a	360	10
230.4.l	\(\chi_{230}(7, \cdot)\)	230.4.l.a	720	20

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(230))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(230)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)