Space of modular forms of level 13 and weight 4

• Label: 13.4
• Level: 13
• Weight: 4
• Dimension: 15
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 56
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(13))\).

	Total	New	Old
Modular forms	27	25	2
Cusp forms	15	15	0
Eisenstein series	12	10	2

Trace form

15 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 6 * q^5 - 6 * q^6 - 42 * q^7 - 78 * q^8 - 6 * q^9 + 84 * q^10 + 54 * q^11 + 228 * q^12 + 138 * q^13 + 108 * q^14 + 66 * q^15 - 6 * q^16 - 195 * q^17 - 834 * q^18 - 450 * q^19 - 522 * q^20 - 6 * q^21 + 384 * q^22 + 222 * q^23 + 1050 * q^24 + 363 * q^25 + 744 * q^26 + 816 * q^27 - 60 * q^28 - 435 * q^29 - 582 * q^30 - 318 * q^31 - 660 * q^32 - 606 * q^33 - 702 * q^34 - 6 * q^35 - 162 * q^36 + 177 * q^37 + 1356 * q^38 + 66 * q^39 - 228 * q^40 - 477 * q^41 - 636 * q^42 - 426 * q^43 + 228 * q^44 + 279 * q^45 + 822 * q^46 + 126 * q^47 - 390 * q^48 + 966 * q^49 - 102 * q^50 - 396 * q^51 - 336 * q^52 + 936 * q^53 + 720 * q^54 + 1398 * q^55 + 996 * q^56 + 1158 * q^57 + 1020 * q^58 + 486 * q^59 + 1152 * q^60 - 1137 * q^61 - 2622 * q^62 - 3186 * q^63 - 4692 * q^64 - 4065 * q^65 - 4152 * q^66 - 918 * q^67 + 1320 * q^68 + 2022 * q^69 + 1980 * q^70 + 1938 * q^71 + 2940 * q^72 + 2154 * q^73 + 2568 * q^74 + 612 * q^75 - 1842 * q^76 + 372 * q^77 + 2940 * q^78 - 972 * q^79 + 3384 * q^80 + 456 * q^81 + 3552 * q^82 + 3426 * q^83 + 2268 * q^84 + 1011 * q^85 - 2808 * q^86 - 3906 * q^87 - 444 * q^88 - 3726 * q^89 - 6936 * q^90 - 2730 * q^91 - 4812 * q^92 - 4194 * q^93 - 1722 * q^94 - 1962 * q^95 + 1548 * q^96 + 1806 * q^97 - 2730 * q^98 + 5190 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.4.a	\(\chi_{13}(1, \cdot)\)	13.4.a.a	1	1
		13.4.a.b	2
13.4.b	\(\chi_{13}(12, \cdot)\)	13.4.b.a	2	1
13.4.c	\(\chi_{13}(3, \cdot)\)	13.4.c.a	2	2
		13.4.c.b	4
13.4.e	\(\chi_{13}(4, \cdot)\)	13.4.e.a	2	2
		13.4.e.b	2