Space of modular forms of level 15 and weight 4

• Label: 15.4
• Level: 15
• Weight: 4
• Dimension: 14
• Nonzero newspaces: 3
• Newform subspaces: 4
• Sturm bound: 64
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(15))\).

	Total	New	Old
Modular forms	32	22	10
Cusp forms	16	14	2
Eisenstein series	16	8	8

Trace form

14 * q + 4 * q^2 - 6 * q^3 - 24 * q^4 + 6 * q^5 - 20 * q^7 - 36 * q^8 - 18 * q^9 - 96 * q^10 - 56 * q^11 + 108 * q^12 + 164 * q^13 + 264 * q^14 + 174 * q^15 + 304 * q^16 + 40 * q^17 - 204 * q^18 - 256 * q^19 - 436 * q^20 - 588 * q^21 - 520 * q^22 - 288 * q^23 - 288 * q^24 + 86 * q^25 + 232 * q^26 + 702 * q^27 + 696 * q^28 + 788 * q^29 + 1116 * q^30 + 632 * q^31 + 116 * q^32 - 12 * q^33 - 568 * q^34 - 520 * q^35 - 696 * q^36 - 1260 * q^37 - 392 * q^38 - 624 * q^39 - 152 * q^40 - 364 * q^41 + 288 * q^42 + 452 * q^43 + 728 * q^44 + 126 * q^45 + 392 * q^46 + 232 * q^47 - 780 * q^48 + 150 * q^49 - 596 * q^50 - 444 * q^51 + 144 * q^52 + 112 * q^53 - 216 * q^54 - 24 * q^55 + 996 * q^57 + 56 * q^58 + 496 * q^59 + 576 * q^60 + 1116 * q^61 + 312 * q^62 + 1392 * q^63 + 1224 * q^64 + 688 * q^65 + 1296 * q^66 + 124 * q^67 + 152 * q^68 + 144 * q^69 - 1560 * q^70 - 688 * q^71 - 2124 * q^72 - 2980 * q^73 - 3376 * q^74 - 3486 * q^75 - 3920 * q^76 - 1728 * q^77 - 960 * q^78 - 1520 * q^79 + 1004 * q^80 + 774 * q^81 + 3912 * q^82 + 1368 * q^83 + 2496 * q^84 + 4092 * q^85 + 4384 * q^86 - 756 * q^87 + 2184 * q^88 - 876 * q^89 + 384 * q^90 + 1592 * q^91 + 1056 * q^92 + 1944 * q^93 + 3416 * q^94 + 3304 * q^95 + 2928 * q^96 + 2484 * q^97 + 404 * q^98 + 1008 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.4.a	\(\chi_{15}(1, \cdot)\)	15.4.a.a	1	1
		15.4.a.b	1
15.4.b	\(\chi_{15}(4, \cdot)\)	15.4.b.a	4	1
15.4.e	\(\chi_{15}(2, \cdot)\)	15.4.e.a	8	2

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

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