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Properties

Label 95.3
Level 95
Weight 3
Dimension 606
Nonzero newspaces 9
Newform subspaces 12
Sturm bound 2160
Trace bound 2

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Defining parameters

Level: \( N \) = \( 95 = 5 \cdot 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 12 \)
Sturm bound: \(2160\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(95))\).

Total New Old
Modular forms 792 706 86
Cusp forms 648 606 42
Eisenstein series 144 100 44

Trace form

\( 606 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 27 q^{5} - 54 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \) \( 606 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 27 q^{5} - 54 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 27 q^{10} - 54 q^{11} - 162 q^{12} - 138 q^{13} - 162 q^{14} - 81 q^{15} - 198 q^{16} - 36 q^{17} - 36 q^{18} + 24 q^{19} + 18 q^{20} + 72 q^{21} + 198 q^{22} + 72 q^{23} + 414 q^{24} + 99 q^{25} + 234 q^{26} + 18 q^{27} - 264 q^{28} - 306 q^{29} - 468 q^{30} - 270 q^{31} - 468 q^{32} - 450 q^{33} - 288 q^{34} - 99 q^{35} - 306 q^{36} - 36 q^{37} + 108 q^{38} + 180 q^{39} + 198 q^{40} + 90 q^{41} + 882 q^{42} + 336 q^{43} - 36 q^{44} + 108 q^{45} + 36 q^{46} - 144 q^{47} + 360 q^{48} + 120 q^{49} - 108 q^{50} - 252 q^{51} - 546 q^{52} - 234 q^{53} - 396 q^{54} - 63 q^{55} - 72 q^{56} + 72 q^{57} + 108 q^{58} + 252 q^{59} + 216 q^{60} - 534 q^{61} - 540 q^{62} - 666 q^{63} - 546 q^{64} - 162 q^{65} + 90 q^{66} - 708 q^{67} + 612 q^{68} - 180 q^{69} - 63 q^{70} + 468 q^{71} + 324 q^{72} - 240 q^{73} - 234 q^{74} - 36 q^{75} + 126 q^{76} + 630 q^{77} + 1746 q^{78} + 1194 q^{79} + 2745 q^{80} + 1854 q^{81} + 2736 q^{82} + 1152 q^{83} + 4086 q^{84} + 1665 q^{85} + 1908 q^{86} + 2718 q^{87} + 2934 q^{88} + 1764 q^{89} + 1908 q^{90} + 1698 q^{91} + 1800 q^{92} + 1206 q^{93} - 756 q^{95} - 3132 q^{96} - 1332 q^{97} - 3564 q^{98} - 2502 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(95))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
95.3.c \(\chi_{95}(56, \cdot)\) 95.3.c.a 12 1
95.3.d \(\chi_{95}(94, \cdot)\) 95.3.d.a 2 1
95.3.d.b 4
95.3.d.c 4
95.3.d.d 8
95.3.f \(\chi_{95}(58, \cdot)\) 95.3.f.a 36 2
95.3.h \(\chi_{95}(69, \cdot)\) 95.3.h.a 36 2
95.3.j \(\chi_{95}(31, \cdot)\) 95.3.j.a 24 2
95.3.m \(\chi_{95}(7, \cdot)\) 95.3.m.a 72 4
95.3.n \(\chi_{95}(21, \cdot)\) 95.3.n.a 84 6
95.3.o \(\chi_{95}(14, \cdot)\) 95.3.o.a 108 6
95.3.q \(\chi_{95}(17, \cdot)\) 95.3.q.a 216 12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(95)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)