Space of modular forms of level 15 and weight 9

• Label: 15.9
• Level: 15
• Weight: 9
• Dimension: 40
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 144
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(15))\).

	Total	New	Old
Modular forms	72	44	28
Cusp forms	56	40	16
Eisenstein series	16	4	12

Trace form

40 * q - 112 * q^3 + 984 * q^4 - 444 * q^5 - 7808 * q^6 + 11696 * q^7 + 17460 * q^8 - 5780 * q^9 - 48276 * q^10 - 23616 * q^11 + 18868 * q^12 + 77956 * q^13 - 75136 * q^15 + 76544 * q^16 + 573300 * q^17 - 419800 * q^18 - 363320 * q^19 - 863436 * q^20 - 150528 * q^21 + 895240 * q^22 + 651480 * q^23 + 1695528 * q^24 - 576464 * q^25 - 448848 * q^26 - 335512 * q^27 - 6908664 * q^28 + 6063316 * q^30 + 5577544 * q^31 + 641460 * q^32 - 2548640 * q^33 - 3054632 * q^34 + 841080 * q^35 - 5027488 * q^36 + 1065276 * q^37 + 8139840 * q^38 + 5607656 * q^39 - 5496592 * q^40 - 14740104 * q^41 - 15036720 * q^42 + 2925856 * q^43 + 9585976 * q^45 + 7311496 * q^46 + 26529600 * q^47 + 26074588 * q^48 + 14661516 * q^49 - 38452896 * q^50 - 33390872 * q^51 + 5202936 * q^52 + 16612140 * q^53 - 43192496 * q^54 - 28324224 * q^55 + 10752000 * q^56 + 1857896 * q^57 + 59211880 * q^58 - 2447144 * q^60 - 53442552 * q^61 - 35190840 * q^62 + 18759576 * q^63 + 62748552 * q^64 + 125689188 * q^65 + 130603856 * q^66 + 190736 * q^67 - 197811840 * q^68 - 47411256 * q^69 - 58334760 * q^70 - 85681968 * q^71 + 15990540 * q^72 - 180800684 * q^73 - 27564136 * q^75 + 53978336 * q^76 + 97175880 * q^77 + 192097600 * q^78 + 443479040 * q^79 + 339741204 * q^80 + 14471320 * q^81 + 21335160 * q^82 - 208234800 * q^83 - 725704584 * q^84 - 463414188 * q^85 - 187512576 * q^86 - 242620600 * q^87 - 346568280 * q^88 + 453645764 * q^90 + 382700992 * q^91 + 652331400 * q^92 + 623199456 * q^93 + 725214088 * q^94 - 74686896 * q^95 + 460479584 * q^96 - 397196244 * q^97 - 50186520 * q^98 - 674325280 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.9.c	\(\chi_{15}(11, \cdot)\)	15.9.c.a	10	1
15.9.d	\(\chi_{15}(14, \cdot)\)	15.9.d.a	1	1
		15.9.d.b	1
		15.9.d.c	12
15.9.f	\(\chi_{15}(7, \cdot)\)	15.9.f.a	16	2

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

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