Space of modular forms of level 7 and weight 10

• Label: 7.10
• Level: 7
• Weight: 10
• Dimension: 15
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 40
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 7 \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(7))\).

	Total	New	Old
Modular forms	21	19	2
Cusp forms	15	15	0
Eisenstein series	6	4	2

Trace form

15 * q - 3 * q^2 + 159 * q^3 - 3 * q^4 + 849 * q^5 - 7782 * q^6 + 1365 * q^7 + 50943 * q^8 - 50697 * q^9 - 50178 * q^10 + 74085 * q^11 + 81354 * q^12 - 365988 * q^13 + 25305 * q^14 + 44562 * q^15 + 804273 * q^16 + 877455 * q^17 - 954093 * q^18 - 718695 * q^19 - 1798944 * q^20 - 1149687 * q^21 - 1731852 * q^22 + 5302623 * q^23 + 10301394 * q^24 + 3850851 * q^25 - 8733228 * q^26 - 20578290 * q^27 - 16929339 * q^28 + 9370734 * q^29 + 32707014 * q^30 + 24515937 * q^31 + 20243007 * q^32 - 34211217 * q^33 - 69138018 * q^34 - 34642167 * q^35 + 30467433 * q^36 + 71698155 * q^37 + 114349800 * q^38 - 5872230 * q^39 - 109547520 * q^40 - 86960958 * q^41 - 161756154 * q^42 + 44269920 * q^43 + 178065924 * q^44 + 137211210 * q^45 + 87626046 * q^46 - 60054321 * q^47 - 197149314 * q^48 - 20200593 * q^49 - 11659107 * q^50 + 77993031 * q^51 + 56451612 * q^52 - 13401909 * q^53 - 13843902 * q^54 - 168072438 * q^55 + 142817871 * q^56 - 81458118 * q^57 - 139251342 * q^58 - 2882805 * q^59 + 29006124 * q^60 + 122988189 * q^61 + 475392360 * q^62 + 229140891 * q^63 - 36739647 * q^64 - 343809606 * q^65 - 927999018 * q^66 - 623805003 * q^67 + 941394258 * q^68 + 1386338886 * q^69 + 358585626 * q^70 - 685727712 * q^71 - 1839019713 * q^72 - 1014197529 * q^73 - 95367408 * q^74 + 923197398 * q^75 + 2112827346 * q^76 + 1818829131 * q^77 + 894536160 * q^78 - 1018942977 * q^79 - 2340781872 * q^80 - 69910596 * q^81 - 389441682 * q^82 - 801356430 * q^83 + 105840882 * q^84 - 585705750 * q^85 - 1976461080 * q^86 - 934468602 * q^87 + 1123814592 * q^88 + 2804638671 * q^89 + 3997968636 * q^90 + 742843332 * q^91 - 940148952 * q^92 + 478677063 * q^93 + 963200754 * q^94 - 2295446583 * q^95 - 2823517662 * q^96 - 1410444126 * q^97 - 2318361843 * q^98 - 2392338492 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.10.a	\(\chi_{7}(1, \cdot)\)	7.10.a.a	2	1
		7.10.a.b	3
7.10.c	\(\chi_{7}(2, \cdot)\)	7.10.c.a	10	2