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Properties

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

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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

\( 17 q + 45 q^{2} - 264 q^{3} + 7037 q^{4} - 17256 q^{5} + 58746 q^{6} - 17311 q^{7} - 141849 q^{8} + 381645 q^{9} + O(q^{10}) \) \( 17 q + 45 q^{2} - 264 q^{3} + 7037 q^{4} - 17256 q^{5} + 58746 q^{6} - 17311 q^{7} - 141849 q^{8} + 381645 q^{9} + 1154190 q^{10} - 2791440 q^{11} + 1646274 q^{12} + 1973734 q^{13} - 3504711 q^{14} - 10721544 q^{15} + 2189009 q^{16} + 13252584 q^{17} + 1777803 q^{18} - 1466144 q^{19} - 10978128 q^{20} + 49115178 q^{21} + 71686572 q^{22} - 92756136 q^{23} - 213893286 q^{24} + 76762787 q^{25} + 97330380 q^{26} + 281112960 q^{27} + 157873541 q^{28} - 320463018 q^{29} - 601742946 q^{30} - 184880960 q^{31} - 309843033 q^{32} + 492217746 q^{33} + 1640460894 q^{34} + 1095988362 q^{35} - 1821580863 q^{36} - 793179776 q^{37} - 1617474528 q^{38} - 1130745672 q^{39} + 3163346808 q^{40} + 3819483402 q^{41} + 4167913806 q^{42} + 564765508 q^{43} - 9824081244 q^{44} - 11798282142 q^{45} - 1215818466 q^{46} + 1964478816 q^{47} + 18823193790 q^{48} + 13388934881 q^{49} - 1614460275 q^{50} - 20383198332 q^{51} - 32531287124 q^{52} + 2633365776 q^{53} + 30575708682 q^{54} + 27598490232 q^{55} + 19943834799 q^{56} - 10938282300 q^{57} - 37517847102 q^{58} - 17226660120 q^{59} - 20448907500 q^{60} + 2738389072 q^{61} + 59455076424 q^{62} + 33131281869 q^{63} - 32750990767 q^{64} - 19139239224 q^{65} - 40046765778 q^{66} - 21412621448 q^{67} + 30069715074 q^{68} + 34942411548 q^{69} + 52698639882 q^{70} - 45083296056 q^{71} - 37474428993 q^{72} - 18847629008 q^{73} + 26618623680 q^{74} + 29010032700 q^{75} - 17755766126 q^{76} - 47083695246 q^{77} + 62336072400 q^{78} - 41189816840 q^{79} + 16324534368 q^{80} + 69614307423 q^{81} - 39612369258 q^{82} + 28016437260 q^{83} - 104718871278 q^{84} + 156178272480 q^{85} + 182419354368 q^{86} + 83179109640 q^{87} - 25344135744 q^{88} - 241823243712 q^{89} - 635276376276 q^{90} - 129451136570 q^{91} - 26224247064 q^{92} + 541378170102 q^{93} + 742570197546 q^{94} + 24651729312 q^{95} - 335954751342 q^{96} - 664774151678 q^{97} - 575878505979 q^{98} + 208612261332 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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