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Properties

Label 95.5
Level 95
Weight 5
Dimension 1262
Nonzero newspaces 9
Newform subspaces 13
Sturm bound 3600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 95 = 5 \cdot 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 13 \)
Sturm bound: \(3600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(95))\).

Total New Old
Modular forms 1512 1362 150
Cusp forms 1368 1262 106
Eisenstein series 144 100 44

Trace form

\( 1262 q - 14 q^{2} + 6 q^{3} - 18 q^{4} - 107 q^{5} - 102 q^{6} + 86 q^{7} + 102 q^{8} - 18 q^{9} + O(q^{10}) \) \( 1262 q - 14 q^{2} + 6 q^{3} - 18 q^{4} - 107 q^{5} - 102 q^{6} + 86 q^{7} + 102 q^{8} - 18 q^{9} - 7 q^{10} - 22 q^{11} - 2082 q^{12} - 454 q^{13} + 1710 q^{14} + 1947 q^{15} + 4634 q^{16} + 580 q^{17} - 72 q^{18} - 1572 q^{19} - 3486 q^{20} - 5460 q^{21} - 6098 q^{22} - 1244 q^{23} - 5202 q^{24} - 853 q^{25} + 4514 q^{26} - 306 q^{27} - 152 q^{28} - 1746 q^{29} + 3864 q^{30} + 3274 q^{31} + 14956 q^{32} + 21390 q^{33} + 15912 q^{34} + 5245 q^{35} + 11934 q^{36} + 968 q^{37} - 9828 q^{38} - 16020 q^{39} - 9102 q^{40} - 2806 q^{41} - 51870 q^{42} - 33988 q^{43} - 60876 q^{44} - 19926 q^{45} - 16052 q^{46} - 1436 q^{47} + 62952 q^{48} + 34260 q^{49} + 50140 q^{50} + 58236 q^{51} + 54230 q^{52} + 34258 q^{53} + 20988 q^{54} + 4537 q^{55} - 6312 q^{56} - 8028 q^{57} - 14244 q^{58} - 29448 q^{59} - 74256 q^{60} - 103502 q^{61} - 107404 q^{62} - 60498 q^{63} - 56514 q^{64} - 23132 q^{65} + 20346 q^{66} + 71120 q^{67} + 88868 q^{68} + 109872 q^{69} + 93417 q^{70} + 127736 q^{71} + 211788 q^{72} + 63740 q^{73} + 20862 q^{74} + 18564 q^{75} - 32274 q^{76} - 13558 q^{77} + 29418 q^{78} - 59262 q^{79} + 48445 q^{80} - 138978 q^{81} - 241400 q^{82} - 108116 q^{83} - 316026 q^{84} - 136915 q^{85} - 121156 q^{86} - 189378 q^{87} - 165282 q^{88} - 14112 q^{89} - 135432 q^{90} + 105154 q^{91} + 99496 q^{92} + 136110 q^{93} - 66150 q^{95} - 98364 q^{96} - 15268 q^{97} + 21728 q^{98} + 128070 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(95))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
95.5.c \(\chi_{95}(56, \cdot)\) 95.5.c.a 28 1
95.5.d \(\chi_{95}(94, \cdot)\) 95.5.d.a 2 1
95.5.d.b 2
95.5.d.c 2
95.5.d.d 4
95.5.d.e 28
95.5.f \(\chi_{95}(58, \cdot)\) 95.5.f.a 72 2
95.5.h \(\chi_{95}(69, \cdot)\) 95.5.h.a 76 2
95.5.j \(\chi_{95}(31, \cdot)\) 95.5.j.a 56 2
95.5.m \(\chi_{95}(7, \cdot)\) 95.5.m.a 152 4
95.5.n \(\chi_{95}(21, \cdot)\) 95.5.n.a 156 6
95.5.o \(\chi_{95}(14, \cdot)\) 95.5.o.a 228 6
95.5.q \(\chi_{95}(17, \cdot)\) 95.5.q.a 456 12

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(95)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)