Space of modular forms of level 15 and weight 11

• Label: 15.11
• Level: 15
• Weight: 11
• Dimension: 52
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 176
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(176\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(15))\).

	Total	New	Old
Modular forms	88	56	32
Cusp forms	72	52	20
Eisenstein series	16	4	12

Trace form

52 * q - 64 * q^2 + 44 * q^3 - 1224 * q^4 + 10676 * q^5 + 8896 * q^6 - 39944 * q^7 - 39948 * q^8 + 171460 * q^9 + 344524 * q^10 + 32080 * q^11 - 576380 * q^12 + 630056 * q^13 - 467956 * q^15 + 2468864 * q^16 + 347360 * q^17 - 4503592 * q^18 + 4763640 * q^19 + 24132564 * q^20 + 1701888 * q^21 - 37749400 * q^22 - 30995704 * q^23 - 12121848 * q^24 + 19687636 * q^25 + 80977840 * q^26 + 13322636 * q^27 - 115886808 * q^28 - 21240284 * q^30 + 37323864 * q^31 - 81249676 * q^32 - 101522456 * q^33 + 41699032 * q^34 + 91578920 * q^35 + 554674688 * q^36 - 180538824 * q^37 + 44187744 * q^38 - 333949936 * q^39 - 657800592 * q^40 + 149264920 * q^41 + 1467214272 * q^42 + 592983800 * q^43 - 383741684 * q^45 - 3021287288 * q^46 - 257112832 * q^47 + 647854972 * q^48 + 1993978364 * q^49 + 909704384 * q^50 + 631338256 * q^51 - 720112008 * q^52 - 152646064 * q^53 - 4481249264 * q^54 - 171284304 * q^55 + 1735516800 * q^56 + 2802185360 * q^57 + 255965768 * q^58 - 3652152344 * q^60 - 2417511896 * q^61 - 969372632 * q^62 + 462574440 * q^63 + 7423253768 * q^64 + 7250334488 * q^65 + 1315846640 * q^66 - 14538445208 * q^67 - 12869460704 * q^68 + 1383058176 * q^69 + 10163849400 * q^70 + 7511442640 * q^71 + 3099955404 * q^72 + 12126056384 * q^73 - 1299366676 * q^75 + 7697464096 * q^76 - 13264676792 * q^77 - 9657137120 * q^78 - 14729216080 * q^79 - 15692039116 * q^80 - 16436158388 * q^81 + 41493340248 * q^82 + 30753878864 * q^83 + 26957446584 * q^84 - 4963698488 * q^85 - 46532117120 * q^86 - 8686965784 * q^87 - 9160290648 * q^88 + 6225772724 * q^90 + 37463722736 * q^91 + 30045377384 * q^92 - 15624450624 * q^93 - 94908576248 * q^94 - 58265269776 * q^95 - 33272381152 * q^96 - 887505288 * q^97 + 54432471592 * q^98 + 79216068560 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.11.c	\(\chi_{15}(11, \cdot)\)	15.11.c.a	14	1
15.11.d	\(\chi_{15}(14, \cdot)\)	15.11.d.a	1	1
		15.11.d.b	1
		15.11.d.c	16
15.11.f	\(\chi_{15}(7, \cdot)\)	15.11.f.a	20	2

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

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