Space of modular forms of level 45 and weight 11

• Label: 45.11
• Level: 45
• Weight: 11
• Dimension: 508
• Nonzero newspaces: 6
• Newform subspaces: 8
• Sturm bound: 1584
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1584\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(45))\).

	Total	New	Old
Modular forms	752	536	216
Cusp forms	688	508	180
Eisenstein series	64	28	36

Trace form

508 * q + 32 * q^2 - 110 * q^3 + 390 * q^4 - 10300 * q^5 + 10550 * q^6 + 86664 * q^7 + 13824 * q^8 + 66794 * q^9 - 222418 * q^10 + 635230 * q^11 - 2316988 * q^12 - 1136360 * q^13 + 4269144 * q^14 + 1107994 * q^15 - 5293086 * q^16 - 3831052 * q^17 + 12932656 * q^18 - 5543476 * q^19 - 12588414 * q^20 + 5149392 * q^21 + 13259934 * q^22 + 7667420 * q^23 + 28196430 * q^24 + 44922616 * q^25 - 58633652 * q^26 - 42330692 * q^27 + 32417872 * q^28 + 82767900 * q^29 + 208651814 * q^30 - 180648060 * q^31 - 120335674 * q^32 - 124734586 * q^33 - 129007534 * q^34 - 177202948 * q^35 + 314496274 * q^36 + 167719016 * q^37 + 1474914774 * q^38 - 144557660 * q^39 - 348496118 * q^40 - 923310758 * q^41 + 81290748 * q^42 - 550076258 * q^43 - 15682564 * q^45 + 4134809640 * q^46 + 1445519432 * q^47 - 251315698 * q^48 - 3126518442 * q^49 - 2167203400 * q^50 - 1472037766 * q^51 - 2213943448 * q^52 + 2643535496 * q^53 + 6281353166 * q^54 + 2029833424 * q^55 + 1436630292 * q^56 + 1372395142 * q^57 - 6807955000 * q^58 - 10385857014 * q^59 - 4821258418 * q^60 + 4027822612 * q^61 + 6059815372 * q^62 + 9457785456 * q^63 + 8876256252 * q^64 + 2367776378 * q^65 + 10184076004 * q^66 + 283144338 * q^67 - 37032521882 * q^68 - 21490886448 * q^69 - 2916230352 * q^70 - 1897725152 * q^71 + 30468966234 * q^72 + 1669806460 * q^73 + 19553516244 * q^74 + 9814760296 * q^75 + 1116326446 * q^76 - 7580167532 * q^77 - 34695810808 * q^78 - 3572353436 * q^79 - 33424807840 * q^80 - 11977873690 * q^81 + 6438050548 * q^82 + 6810976244 * q^83 + 44780014476 * q^84 - 8616026002 * q^85 + 16856442766 * q^86 - 12276765452 * q^87 + 4180897254 * q^88 - 33875218598 * q^90 - 30525596544 * q^91 - 59668699384 * q^92 - 41115349512 * q^93 + 112521640100 * q^94 + 48892628874 * q^95 - 15548944160 * q^96 - 30566842234 * q^97 + 83627444182 * q^98 + 91295231056 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.11.c	\(\chi_{45}(26, \cdot)\)	45.11.c.a	12	1
45.11.d	\(\chi_{45}(44, \cdot)\)	45.11.d.a	20	1
45.11.g	\(\chi_{45}(28, \cdot)\)	45.11.g.a	8	2
		45.11.g.b	20
		45.11.g.c	20
45.11.h	\(\chi_{45}(14, \cdot)\)	45.11.h.a	116	2
45.11.i	\(\chi_{45}(11, \cdot)\)	45.11.i.a	80	2
45.11.k	\(\chi_{45}(7, \cdot)\)	45.11.k.a	232	4

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)