Space of modular forms of level 7 and weight 12

• Label: 7.12
• Level: 7
• Weight: 12
• Dimension: 17
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 48
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 7 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(7))\).

	Total	New	Old
Modular forms	25	21	4
Cusp forms	19	17	2
Eisenstein series	6	4	2

Trace form

17 * q + 45 * q^2 - 264 * q^3 + 7037 * q^4 - 17256 * q^5 + 58746 * q^6 - 17311 * q^7 - 141849 * q^8 + 381645 * q^9 + 1154190 * q^10 - 2791440 * q^11 + 1646274 * q^12 + 1973734 * q^13 - 3504711 * q^14 - 10721544 * q^15 + 2189009 * q^16 + 13252584 * q^17 + 1777803 * q^18 - 1466144 * q^19 - 10978128 * q^20 + 49115178 * q^21 + 71686572 * q^22 - 92756136 * q^23 - 213893286 * q^24 + 76762787 * q^25 + 97330380 * q^26 + 281112960 * q^27 + 157873541 * q^28 - 320463018 * q^29 - 601742946 * q^30 - 184880960 * q^31 - 309843033 * q^32 + 492217746 * q^33 + 1640460894 * q^34 + 1095988362 * q^35 - 1821580863 * q^36 - 793179776 * q^37 - 1617474528 * q^38 - 1130745672 * q^39 + 3163346808 * q^40 + 3819483402 * q^41 + 4167913806 * q^42 + 564765508 * q^43 - 9824081244 * q^44 - 11798282142 * q^45 - 1215818466 * q^46 + 1964478816 * q^47 + 18823193790 * q^48 + 13388934881 * q^49 - 1614460275 * q^50 - 20383198332 * q^51 - 32531287124 * q^52 + 2633365776 * q^53 + 30575708682 * q^54 + 27598490232 * q^55 + 19943834799 * q^56 - 10938282300 * q^57 - 37517847102 * q^58 - 17226660120 * q^59 - 20448907500 * q^60 + 2738389072 * q^61 + 59455076424 * q^62 + 33131281869 * q^63 - 32750990767 * q^64 - 19139239224 * q^65 - 40046765778 * q^66 - 21412621448 * q^67 + 30069715074 * q^68 + 34942411548 * q^69 + 52698639882 * q^70 - 45083296056 * q^71 - 37474428993 * q^72 - 18847629008 * q^73 + 26618623680 * q^74 + 29010032700 * q^75 - 17755766126 * q^76 - 47083695246 * q^77 + 62336072400 * q^78 - 41189816840 * q^79 + 16324534368 * q^80 + 69614307423 * q^81 - 39612369258 * q^82 + 28016437260 * q^83 - 104718871278 * q^84 + 156178272480 * q^85 + 182419354368 * q^86 + 83179109640 * q^87 - 25344135744 * q^88 - 241823243712 * q^89 - 635276376276 * q^90 - 129451136570 * q^91 - 26224247064 * q^92 + 541378170102 * q^93 + 742570197546 * q^94 + 24651729312 * q^95 - 335954751342 * q^96 - 664774151678 * q^97 - 575878505979 * q^98 + 208612261332 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)

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
7.12.a	\(\chi_{7}(1, \cdot)\)	7.12.a.a	2	1
		7.12.a.b	3
7.12.c	\(\chi_{7}(2, \cdot)\)	7.12.c.a	12	2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(7))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(7)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)