Space of modular forms of level 13 and weight 9

• Label: 13.9
• Level: 13
• Weight: 9
• Dimension: 50
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 126
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 13 \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(126\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(13))\).

	Total	New	Old
Modular forms	62	62	0
Cusp forms	50	50	0
Eisenstein series	12	12	0

Trace form

50 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 6 * q^5 - 6 * q^6 + 2524 * q^7 - 6 * q^8 + 17490 * q^9 - 26886 * q^10 - 25080 * q^11 + 86094 * q^13 + 105972 * q^14 - 6810 * q^15 - 327686 * q^16 + 97644 * q^17 - 784608 * q^18 + 473602 * q^19 + 1422066 * q^20 + 65592 * q^21 - 809556 * q^22 - 711654 * q^23 - 2383062 * q^24 + 1910964 * q^26 + 3751188 * q^27 + 4005248 * q^28 - 2657418 * q^29 - 6200118 * q^30 - 99196 * q^31 + 1902216 * q^32 + 999108 * q^33 + 4060674 * q^34 - 1397796 * q^35 - 11372454 * q^36 - 8096248 * q^37 + 13660674 * q^39 + 2352828 * q^40 - 1145094 * q^41 + 14113128 * q^42 + 18199452 * q^43 + 1762716 * q^44 - 3863376 * q^45 - 23702154 * q^46 - 21423408 * q^47 - 30089718 * q^48 - 18234288 * q^49 + 30161304 * q^50 - 40945708 * q^52 + 24470232 * q^53 + 80265120 * q^54 + 74753604 * q^55 + 84926940 * q^56 + 22501356 * q^57 - 46153494 * q^58 - 56069124 * q^59 - 225562428 * q^60 - 90554442 * q^61 + 2935614 * q^62 - 59182548 * q^63 + 54879114 * q^65 + 158753424 * q^66 + 31422418 * q^67 + 351553224 * q^68 + 163279656 * q^69 + 90147084 * q^70 - 46423914 * q^71 - 348800880 * q^72 - 175935974 * q^73 - 390463386 * q^74 - 364524840 * q^75 - 331167530 * q^76 + 464119008 * q^78 + 287989080 * q^79 + 897035604 * q^80 + 276106674 * q^81 + 272314014 * q^82 + 147421632 * q^83 - 118954092 * q^84 - 71261994 * q^85 - 611519460 * q^86 - 955994634 * q^87 - 1180586364 * q^88 - 422276046 * q^89 + 484120936 * q^91 + 1153271580 * q^92 + 1306731180 * q^93 + 1241176758 * q^94 + 318589986 * q^95 - 304944120 * q^96 + 101151350 * q^97 - 699182022 * q^98 - 1484420112 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.9.d	\(\chi_{13}(5, \cdot)\)	13.9.d.a	18	2
13.9.f	\(\chi_{13}(2, \cdot)\)	13.9.f.a	32	4