Space of modular forms of level 13 and weight 11

• Label: 13.11
• Level: 13
• Weight: 11
• Dimension: 64
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 154
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 13 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(154\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(13))\).

	Total	New	Old
Modular forms	76	76	0
Cusp forms	64	64	0
Eisenstein series	12	12	0

Trace form

64 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 6 * q^5 - 6 * q^6 - 7456 * q^7 + 147450 * q^8 - 157470 * q^9 - 37926 * q^10 + 294228 * q^11 - 1227738 * q^13 - 756108 * q^14 + 1892478 * q^15 + 5242874 * q^16 + 2121648 * q^17 - 13319952 * q^18 + 8292890 * q^19 + 7233522 * q^20 - 32239044 * q^21 - 3943716 * q^22 + 14209650 * q^23 + 66932778 * q^24 - 58420476 * q^26 - 94603764 * q^27 - 42152960 * q^28 + 360834 * q^29 + 386524746 * q^30 + 86481376 * q^31 - 246646872 * q^32 - 358403904 * q^33 - 238255806 * q^34 + 270086184 * q^35 + 862663626 * q^36 - 89948216 * q^37 - 114371022 * q^39 - 1495270404 * q^40 - 40860516 * q^41 + 989137560 * q^42 + 484189248 * q^43 + 755584044 * q^44 - 689980446 * q^45 - 1182412266 * q^46 - 462398580 * q^47 - 384517494 * q^48 + 1432995756 * q^49 + 3784343496 * q^50 - 3761020508 * q^52 - 1251117528 * q^53 - 188393808 * q^54 - 990869016 * q^55 - 784908372 * q^56 + 414004128 * q^57 + 2654091402 * q^58 + 1581718176 * q^59 + 4463727732 * q^60 - 2668039476 * q^61 - 480851634 * q^62 - 7749794544 * q^63 + 10048236228 * q^65 + 11380456848 * q^66 - 7736869390 * q^67 - 13241644584 * q^68 - 8061602724 * q^69 - 10860187908 * q^70 - 2690760114 * q^71 + 21419991744 * q^72 + 15932767610 * q^73 + 17420705862 * q^74 + 2520930528 * q^75 - 2849673610 * q^76 - 15349151712 * q^78 + 947674896 * q^79 - 32231060508 * q^80 - 22109338842 * q^81 - 40275130626 * q^82 - 222571212 * q^83 + 25211545620 * q^84 + 48229514352 * q^85 + 27564684060 * q^86 + 8360182926 * q^87 + 41091238308 * q^88 + 19174360266 * q^89 - 9908224924 * q^91 - 62579932164 * q^92 - 47597893944 * q^93 - 27308083914 * q^94 - 20960240478 * q^95 - 80477408808 * q^96 + 29400101014 * q^97 - 1133576070 * q^98 + 98659951308 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.11.d	\(\chi_{13}(5, \cdot)\)	13.11.d.a	20	2
13.11.f	\(\chi_{13}(2, \cdot)\)	13.11.f.a	44	4