Space of modular forms of level 95 and weight 11

• Label: 95.11
• Level: 95
• Weight: 11
• Dimension: 3230
• Nonzero newspaces: 9
• Newform subspaces: 12
• Sturm bound: 7920
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(7920\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(95))\).

	Total	New	Old
Modular forms	3672	3330	342
Cusp forms	3528	3230	298
Eisenstein series	144	100	44

Trace form

3230 * q - 78 * q^2 - 138 * q^3 - 18 * q^4 + 10653 * q^5 - 34086 * q^6 + 28982 * q^7 - 44058 * q^8 - 18 * q^9 + 322553 * q^10 + 467514 * q^11 + 1259646 * q^12 - 4233658 * q^13 + 3674862 * q^14 + 9215859 * q^15 - 8855590 * q^16 - 7945920 * q^17 - 25608456 * q^18 + 21917892 * q^19 + 53957538 * q^20 + 33952044 * q^21 - 114401234 * q^22 - 69774228 * q^23 + 44789742 * q^24 + 119747399 * q^25 + 122357154 * q^26 - 238181454 * q^27 + 326776 * q^28 - 177911730 * q^29 + 11977752 * q^30 + 122259490 * q^31 + 613050972 * q^32 + 293503470 * q^33 - 373029048 * q^34 - 548906139 * q^35 - 1480729122 * q^36 - 184432276 * q^37 + 1614989388 * q^38 + 1579614228 * q^39 - 151719702 * q^40 - 254735670 * q^41 - 1654851198 * q^42 - 2276310028 * q^43 + 1254448260 * q^44 - 750958722 * q^45 - 1963942196 * q^46 + 1169124468 * q^47 + 3874106616 * q^48 - 464842236 * q^49 - 949666068 * q^50 + 7497085992 * q^51 - 2214130090 * q^52 - 1056153642 * q^53 - 6669100404 * q^54 - 1534788263 * q^55 - 1705831272 * q^56 + 2055683412 * q^57 + 683141820 * q^58 + 7884604512 * q^59 + 9980591736 * q^60 + 19858467754 * q^61 - 1450015836 * q^62 - 28905467490 * q^63 - 43341908034 * q^64 - 2828618412 * q^65 + 18722460858 * q^66 + 23591314568 * q^67 + 40982277972 * q^68 + 22209160320 * q^69 + 7991322537 * q^70 - 27374389728 * q^71 - 72207962244 * q^72 - 22712550076 * q^73 - 20439782370 * q^74 - 10758005436 * q^75 + 34045267566 * q^76 + 48985793970 * q^77 - 1480985814 * q^78 + 32229277842 * q^79 + 48534178125 * q^80 + 27483453918 * q^81 - 17075410184 * q^82 - 6271933980 * q^83 - 161009954298 * q^84 - 108382268695 * q^85 - 106565068212 * q^86 + 7248491838 * q^87 + 124526509950 * q^88 + 98086756392 * q^89 + 149343966288 * q^90 + 15959730178 * q^91 + 4801419480 * q^92 + 70664719206 * q^93 + 7038605574 * q^95 - 69580003260 * q^96 - 90984729568 * q^97 - 351655980144 * q^98 - 249739320438 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(95))\)

We only show spaces with odd 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
95.11.c	\(\chi_{95}(56, \cdot)\)	95.11.c.a	68	1
95.11.d	\(\chi_{95}(94, \cdot)\)	95.11.d.a	2	1
		95.11.d.b	4
		95.11.d.c	4
		95.11.d.d	88
95.11.f	\(\chi_{95}(58, \cdot)\)	95.11.f.a	180	2
95.11.h	\(\chi_{95}(69, \cdot)\)	95.11.h.a	196	2
95.11.j	\(\chi_{95}(31, \cdot)\)	95.11.j.a	136	2
95.11.m	\(\chi_{95}(7, \cdot)\)	95.11.m.a	392	4
95.11.n	\(\chi_{95}(21, \cdot)\)	95.11.n.a	396	6
95.11.o	\(\chi_{95}(14, \cdot)\)	95.11.o.a	588	6
95.11.q	\(\chi_{95}(17, \cdot)\)	95.11.q.a	1176	12

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(95)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)