Space of modular forms of level 15 and weight 16

• Label: 15.16
• Level: 15
• Weight: 16
• Dimension: 82
• Nonzero newspaces: 3
• Newform subspaces: 6
• Sturm bound: 256
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(256\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(15))\).

	Total	New	Old
Modular forms	128	90	38
Cusp forms	112	82	30
Eisenstein series	16	8	8

Trace form

82 * q + 356 * q^2 + 1434 * q^3 - 87112 * q^4 + 469506 * q^5 - 666372 * q^6 + 4407068 * q^7 - 3591684 * q^8 - 28697814 * q^9 + 104366424 * q^10 - 123114616 * q^11 - 137009964 * q^12 + 798189972 * q^13 - 885135288 * q^14 + 364107654 * q^15 - 2074722192 * q^16 - 1399201240 * q^17 + 6043909764 * q^18 + 8466223392 * q^19 - 25144669076 * q^20 + 16408468020 * q^21 + 53064723080 * q^22 - 44825634432 * q^23 - 63010689264 * q^24 + 119219528746 * q^25 + 180227576072 * q^26 - 239320376658 * q^27 + 153550964920 * q^28 - 153769809956 * q^29 + 3699207696 * q^30 - 151838875512 * q^31 + 916209592084 * q^32 + 536731029012 * q^33 - 1235595183064 * q^34 - 1457840489240 * q^35 + 2093267916600 * q^36 + 1772316045028 * q^37 - 1358266064728 * q^38 + 708624706608 * q^39 - 7346422645112 * q^40 + 6062938642156 * q^41 + 7100841936672 * q^42 + 1895261422884 * q^43 - 31608170460296 * q^44 + 1482687149346 * q^45 + 36620697722888 * q^46 + 7498837787528 * q^47 - 18121577303052 * q^48 - 29013541109550 * q^49 - 13165712025316 * q^50 + 10112586061764 * q^51 + 34341617390224 * q^52 - 13011279805552 * q^53 - 8744855277708 * q^54 - 26795442121464 * q^55 + 83535054240960 * q^56 - 20436708350988 * q^57 - 40936271581576 * q^58 - 39965398018192 * q^59 + 40829683929336 * q^60 + 19700838105892 * q^61 + 27671214085608 * q^62 + 21963528050064 * q^63 - 222514006650808 * q^64 + 74732006712128 * q^65 + 206858744805696 * q^66 + 28429092450044 * q^67 + 184364677990648 * q^68 + 62648744298192 * q^69 - 355582779802200 * q^70 - 130041241358288 * q^71 - 331215580280556 * q^72 + 272937883027356 * q^73 + 847264039240672 * q^74 + 696786095694354 * q^75 - 505352478989008 * q^76 - 666245568098592 * q^77 - 1836997173931320 * q^78 - 216934644900160 * q^79 + 1525465120555084 * q^80 + 963664108536042 * q^81 + 529750463326728 * q^82 + 669843947311992 * q^83 - 709079015652192 * q^84 - 2122678541384868 * q^85 - 3199358156478256 * q^86 - 852887723025444 * q^87 + 4442736906596616 * q^88 + 2554763137516092 * q^89 + 4640122920070824 * q^90 - 3837713884765352 * q^91 - 4327487625812736 * q^92 - 3989818956457128 * q^93 - 4021033775460712 * q^94 + 1786787250778664 * q^95 + 12070499514262512 * q^96 + 7219130913825844 * q^97 - 3221164311019244 * q^98 - 1783145866475376 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(15))\)

We only show spaces with even 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
15.16.a	\(\chi_{15}(1, \cdot)\)	15.16.a.a	2	1
		15.16.a.b	2
		15.16.a.c	3
		15.16.a.d	3
15.16.b	\(\chi_{15}(4, \cdot)\)	15.16.b.a	16	1
15.16.e	\(\chi_{15}(2, \cdot)\)	15.16.e.a	56	2

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)