Space of modular forms of level 230 and weight 6

• Label: 230.6
• Level: 230
• Weight: 6
• Dimension: 2410
• Nonzero newspaces: 6
• Sturm bound: 19008
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(19008\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(230))\).

	Total	New	Old
Modular forms	8096	2410	5686
Cusp forms	7744	2410	5334
Eisenstein series	352	0	352

Trace form

2410 * q + 8 * q^2 - 8 * q^3 - 32 * q^4 - 170 * q^5 + 160 * q^6 + 624 * q^7 + 128 * q^8 - 1306 * q^9 + 360 * q^10 + 1480 * q^11 - 128 * q^12 - 228 * q^13 - 3136 * q^14 - 10902 * q^15 - 2560 * q^16 + 14048 * q^17 + 32776 * q^18 + 14284 * q^19 + 448 * q^20 - 50348 * q^21 - 27920 * q^22 - 43712 * q^23 - 4608 * q^24 - 16814 * q^25 + 8064 * q^26 + 99532 * q^27 + 51520 * q^28 + 38864 * q^29 + 57136 * q^30 + 25764 * q^31 + 2048 * q^32 - 213620 * q^33 - 37616 * q^34 - 20670 * q^35 - 14880 * q^36 + 178036 * q^37 + 34720 * q^38 + 190808 * q^39 + 640 * q^40 + 6144 * q^41 - 22784 * q^42 - 145040 * q^43 + 4736 * q^44 - 149340 * q^45 - 9920 * q^46 - 235064 * q^47 - 2048 * q^48 + 5226 * q^49 + 22600 * q^50 + 48248 * q^51 - 3648 * q^52 + 232736 * q^53 - 357200 * q^54 - 12784 * q^55 + 44800 * q^56 + 492044 * q^57 + 280528 * q^58 + 277180 * q^59 + 39968 * q^60 + 645300 * q^61 + 246928 * q^62 + 113572 * q^63 - 8192 * q^64 - 265194 * q^65 - 487360 * q^66 - 399008 * q^67 - 436288 * q^68 - 1183556 * q^69 - 551328 * q^70 - 864220 * q^71 - 50048 * q^72 - 22820 * q^73 + 237744 * q^74 + 220104 * q^75 - 105600 * q^76 + 1425548 * q^77 + 740560 * q^78 + 1990404 * q^79 + 119808 * q^80 + 1852542 * q^81 + 295984 * q^82 + 462248 * q^83 - 77504 * q^84 - 749566 * q^85 - 1085360 * q^86 - 949428 * q^87 - 105984 * q^88 - 614816 * q^89 - 53880 * q^90 - 1227448 * q^91 - 50304 * q^92 - 235936 * q^93 + 316544 * q^94 + 2580102 * q^95 + 40960 * q^96 + 1604980 * q^97 - 16216 * q^98 - 48640 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(230))\)

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
230.6.a	\(\chi_{230}(1, \cdot)\)	230.6.a.a	1	1
		230.6.a.b	2
		230.6.a.c	3
		230.6.a.d	3
		230.6.a.e	3
		230.6.a.f	5
		230.6.a.g	5
		230.6.a.h	6
		230.6.a.i	6
230.6.b	\(\chi_{230}(139, \cdot)\)	230.6.b.a	26	1
		230.6.b.b	30
230.6.e	\(\chi_{230}(137, \cdot)\)	n/a	120	2
230.6.g	\(\chi_{230}(31, \cdot)\)	n/a	400	10
230.6.j	\(\chi_{230}(9, \cdot)\)	n/a	600	10
230.6.l	\(\chi_{230}(7, \cdot)\)	n/a	1200	20

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(230))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(230)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)