Space of modular forms of level 115 and weight 4

• Label: 115.4
• Level: 115
• Weight: 4
• Dimension: 1384
• Nonzero newspaces: 6
• Newform subspaces: 12
• Sturm bound: 4224
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(4224\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(115))\).

	Total	New	Old
Modular forms	1672	1512	160
Cusp forms	1496	1384	112
Eisenstein series	176	128	48

Trace form

1384 * q - 14 * q^2 - 26 * q^3 - 38 * q^4 - 23 * q^5 - 50 * q^6 - 34 * q^7 - 22 * q^8 + 24 * q^9 - 73 * q^10 - 130 * q^11 - 54 * q^12 + 54 * q^13 + 26 * q^14 + 361 * q^15 + 942 * q^16 + 102 * q^17 - 382 * q^18 - 442 * q^19 - 657 * q^20 - 1410 * q^21 - 712 * q^22 - 912 * q^23 - 2684 * q^24 - 435 * q^25 - 810 * q^26 + 46 * q^27 + 586 * q^28 + 518 * q^29 + 1383 * q^30 + 1250 * q^31 + 2458 * q^32 + 1786 * q^33 + 4014 * q^34 + 1457 * q^35 + 5252 * q^36 + 1822 * q^37 + 1988 * q^38 - 134 * q^39 - 1353 * q^40 - 1210 * q^41 - 7186 * q^42 - 4338 * q^43 - 6980 * q^44 - 3222 * q^45 - 8298 * q^46 - 2800 * q^47 - 6454 * q^48 - 3764 * q^49 - 383 * q^50 - 1490 * q^51 - 74 * q^52 + 458 * q^53 + 10178 * q^54 + 4775 * q^55 + 18700 * q^56 + 11458 * q^57 + 15484 * q^58 + 6942 * q^59 + 4197 * q^60 - 86 * q^61 - 4318 * q^62 - 3926 * q^63 - 7446 * q^64 - 4725 * q^65 - 9872 * q^66 - 3178 * q^67 - 18368 * q^68 - 7346 * q^69 - 6114 * q^70 - 7710 * q^71 - 14212 * q^72 - 378 * q^73 + 148 * q^74 + 5829 * q^75 + 12612 * q^76 + 10506 * q^77 + 22294 * q^78 + 8194 * q^79 + 10426 * q^80 + 11852 * q^81 + 10054 * q^82 + 7114 * q^83 + 11710 * q^84 - 675 * q^85 + 522 * q^86 - 18566 * q^87 - 15334 * q^88 - 10942 * q^89 - 17626 * q^90 - 15604 * q^91 - 17416 * q^92 - 23108 * q^93 - 20788 * q^94 - 14763 * q^95 - 49424 * q^96 - 21518 * q^97 - 25006 * q^98 - 21650 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)

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
115.4.a	\(\chi_{115}(1, \cdot)\)	115.4.a.a	1	1
		115.4.a.b	1
		115.4.a.c	2
		115.4.a.d	5
		115.4.a.e	5
		115.4.a.f	8
115.4.b	\(\chi_{115}(24, \cdot)\)	115.4.b.a	34	1
115.4.e	\(\chi_{115}(22, \cdot)\)	115.4.e.a	68	2
115.4.g	\(\chi_{115}(6, \cdot)\)	115.4.g.a	110	10
		115.4.g.b	130
115.4.j	\(\chi_{115}(4, \cdot)\)	115.4.j.a	340	10
115.4.l	\(\chi_{115}(7, \cdot)\)	115.4.l.a	680	20

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(115))\) into lower level spaces

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