Space of modular forms of level 230 and weight 2

• Label: 230.2
• Level: 230
• Weight: 2
• Dimension: 485
• Nonzero newspaces: 6
• Newform subspaces: 15
• Sturm bound: 6336
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 15 \)
Sturm bound:			\(6336\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(230))\).

	Total	New	Old
Modular forms	1760	485	1275
Cusp forms	1409	485	924
Eisenstein series	351	0	351

Trace form

485 * q + q^2 + 4 * q^3 + q^4 + q^5 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 + q^10 + 12 * q^11 + 4 * q^12 + 14 * q^13 + 8 * q^14 - 18 * q^15 + q^16 - 26 * q^17 - 75 * q^18 - 24 * q^19 - 21 * q^20 - 100 * q^21 - 32 * q^22 - 65 * q^23 + 4 * q^24 - 43 * q^25 - 30 * q^26 - 92 * q^27 - 36 * q^28 - 14 * q^29 - 40 * q^30 - 12 * q^31 + q^32 + 4 * q^33 + 18 * q^34 - 14 * q^35 + 13 * q^36 - 50 * q^37 + 20 * q^38 - 32 * q^39 + q^40 - 2 * q^41 + 32 * q^42 - 44 * q^43 + 12 * q^44 - 53 * q^45 + 23 * q^46 - 40 * q^47 + 4 * q^48 - 75 * q^49 + q^50 - 16 * q^51 + 14 * q^52 + 10 * q^53 - 4 * q^54 - 76 * q^55 - 36 * q^56 - 140 * q^57 - 58 * q^58 - 160 * q^59 - 18 * q^60 - 114 * q^61 - 100 * q^62 - 116 * q^63 + q^64 - 140 * q^65 - 128 * q^66 - 20 * q^67 - 70 * q^68 - 128 * q^69 - 80 * q^70 - 148 * q^71 - 75 * q^72 - 14 * q^73 - 138 * q^74 - 172 * q^75 + 20 * q^76 - 124 * q^77 - 76 * q^78 - 140 * q^79 - 21 * q^80 - 143 * q^81 - 46 * q^82 - 92 * q^83 - 12 * q^84 - 48 * q^85 - 12 * q^87 + 12 * q^88 + 46 * q^89 + 13 * q^90 + 24 * q^91 + 23 * q^92 + 128 * q^93 + 48 * q^94 + 42 * q^95 + 4 * q^96 + 186 * q^97 + 145 * q^98 + 244 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)

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
230.2.a	\(\chi_{230}(1, \cdot)\)	230.2.a.a	2	1
		230.2.a.b	2
		230.2.a.c	2
		230.2.a.d	3
230.2.b	\(\chi_{230}(139, \cdot)\)	230.2.b.a	4	1
		230.2.b.b	8
230.2.e	\(\chi_{230}(137, \cdot)\)	230.2.e.a	8	2
		230.2.e.b	8
		230.2.e.c	8
230.2.g	\(\chi_{230}(31, \cdot)\)	230.2.g.a	10	10
		230.2.g.b	20
		230.2.g.c	20
		230.2.g.d	30
230.2.j	\(\chi_{230}(9, \cdot)\)	230.2.j.a	120	10
230.2.l	\(\chi_{230}(7, \cdot)\)	230.2.l.a	240	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(230))\) into lower level spaces

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