Space of modular forms of level 90 and weight 11

• Label: 90.11
• Level: 90
• Weight: 11
• Dimension: 526
• Nonzero newspaces: 6
• Newform subspaces: 14
• Sturm bound: 4752
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 14 \)
Sturm bound:			\(4752\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(90))\).

	Total	New	Old
Modular forms	2224	526	1698
Cusp forms	2096	526	1570
Eisenstein series	128	0	128

Trace form

526 * q - 32 * q^2 + 168 * q^3 - 8192 * q^4 + 17478 * q^5 - 25728 * q^6 - 96416 * q^7 + 16384 * q^8 - 276296 * q^9 + 161952 * q^10 - 635236 * q^11 + 108544 * q^12 + 1120506 * q^13 - 351360 * q^14 - 1880502 * q^15 + 1572864 * q^16 + 9700070 * q^17 + 73472 * q^18 - 5226336 * q^19 - 4280320 * q^20 - 4540788 * q^21 + 6559360 * q^22 + 911192 * q^23 - 5505024 * q^24 + 52791160 * q^25 + 15915840 * q^26 + 58388016 * q^27 + 11769856 * q^28 - 64881612 * q^29 - 37556352 * q^30 + 136917460 * q^31 + 8388608 * q^32 + 61086148 * q^33 + 63619456 * q^34 - 18854764 * q^35 - 118274048 * q^36 - 261285030 * q^37 - 264946816 * q^38 + 684894100 * q^39 + 43401216 * q^40 + 7880876 * q^41 - 616959488 * q^42 + 270638976 * q^43 + 1103200514 * q^45 - 1344734336 * q^46 - 1252373304 * q^47 + 76546048 * q^48 + 2215907124 * q^49 - 2167568608 * q^50 + 1096345128 * q^51 + 289293312 * q^52 + 243198922 * q^53 + 567725952 * q^54 - 2282102156 * q^55 + 209059840 * q^56 - 5474900488 * q^57 - 843792256 * q^58 + 12758790060 * q^59 + 559172608 * q^60 + 356354308 * q^61 + 2232107392 * q^62 - 5886899932 * q^63 + 5905580032 * q^64 - 10581674892 * q^65 - 12077937408 * q^66 + 6365432344 * q^67 + 254538752 * q^68 + 24135395708 * q^69 + 4103045952 * q^70 + 16524671800 * q^71 - 3108765696 * q^72 - 15275492038 * q^73 - 18236245248 * q^74 - 20049467142 * q^75 - 2066771968 * q^76 + 19456569148 * q^77 + 18994995200 * q^78 + 4245576876 * q^79 - 1981808640 * q^80 + 23760644384 * q^81 - 1440442496 * q^82 + 12704135592 * q^83 + 3373928448 * q^84 - 125896090 * q^85 + 14604546048 * q^86 - 29530898924 * q^87 - 3358392320 * q^88 + 25758006784 * q^90 + 79950529056 * q^91 + 466530304 * q^92 + 27583921676 * q^93 - 40706373760 * q^94 - 83861294348 * q^95 - 2449473536 * q^96 + 7747097838 * q^97 + 29100603104 * q^98 - 121816628084 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.11.b	\(\chi_{90}(89, \cdot)\)	90.11.b.a	20	1
90.11.d	\(\chi_{90}(71, \cdot)\)	90.11.d.a	8	1
		90.11.d.b	8
90.11.g	\(\chi_{90}(37, \cdot)\)	90.11.g.a	2	2
		90.11.g.b	2
		90.11.g.c	6
		90.11.g.d	8
		90.11.g.e	10
		90.11.g.f	10
		90.11.g.g	12
90.11.h	\(\chi_{90}(11, \cdot)\)	90.11.h.a	80	2
90.11.j	\(\chi_{90}(29, \cdot)\)	90.11.j.a	120	2
90.11.k	\(\chi_{90}(7, \cdot)\)	90.11.k.a	120	4
		90.11.k.b	120

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(90)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)