Properties

Label 361.2
Level 361
Weight 2
Dimension 5150
Nonzero newspaces 6
Newform subspaces 35
Sturm bound 21660
Trace bound 1

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Defining parameters

Level: \( N \) = \( 361 = 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 35 \)
Sturm bound: \(21660\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(361))\).

Total New Old
Modular forms 5667 5619 48
Cusp forms 5164 5150 14
Eisenstein series 503 469 34

Trace form

\( 5150 q - 156 q^{2} - 157 q^{3} - 160 q^{4} - 159 q^{5} - 165 q^{6} - 161 q^{7} - 168 q^{8} - 166 q^{9} + O(q^{10}) \) \( 5150 q - 156 q^{2} - 157 q^{3} - 160 q^{4} - 159 q^{5} - 165 q^{6} - 161 q^{7} - 168 q^{8} - 166 q^{9} - 171 q^{10} - 165 q^{11} - 157 q^{12} - 143 q^{13} - 141 q^{14} - 141 q^{15} - 112 q^{16} - 153 q^{17} - 120 q^{18} - 141 q^{19} - 267 q^{20} - 143 q^{21} - 135 q^{22} - 159 q^{23} - 141 q^{24} - 148 q^{25} - 159 q^{26} - 151 q^{27} - 131 q^{28} - 147 q^{29} - 99 q^{30} - 149 q^{31} - 126 q^{32} - 93 q^{33} - 117 q^{34} - 129 q^{35} - 28 q^{36} - 137 q^{37} - 99 q^{38} - 245 q^{39} - 81 q^{40} - 159 q^{41} - 69 q^{42} - 119 q^{43} - 93 q^{44} - 69 q^{45} - 63 q^{46} - 111 q^{47} - 25 q^{48} - 132 q^{49} - 48 q^{50} - 117 q^{51} - 119 q^{52} - 135 q^{53} - 111 q^{54} - 153 q^{55} - 39 q^{56} - 117 q^{57} - 315 q^{58} - 123 q^{59} - 15 q^{60} - 83 q^{61} - 51 q^{62} - 89 q^{63} - 4 q^{64} - 39 q^{65} - 9 q^{66} - 35 q^{67} - 27 q^{68} - 51 q^{69} - 9 q^{70} - 99 q^{71} + 48 q^{72} - 59 q^{73} - 87 q^{74} - 91 q^{75} - 72 q^{76} - 195 q^{77} - 33 q^{78} - 29 q^{79} - 15 q^{80} - 40 q^{81} + 63 q^{82} - 111 q^{83} + 55 q^{84} - 45 q^{85} - 87 q^{86} + 15 q^{87} - 9 q^{88} - 81 q^{89} + 27 q^{90} - 97 q^{91} - 87 q^{92} - 77 q^{93} - 63 q^{94} - 99 q^{95} - 117 q^{96} - 125 q^{97} + 18 q^{98} - 39 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
361.2.a \(\chi_{361}(1, \cdot)\) 361.2.a.a 1 1
361.2.a.b 1
361.2.a.c 2
361.2.a.d 2
361.2.a.e 2
361.2.a.f 2
361.2.a.g 3
361.2.a.h 3
361.2.a.i 4
361.2.c \(\chi_{361}(68, \cdot)\) 361.2.c.a 2 2
361.2.c.b 2
361.2.c.c 2
361.2.c.d 4
361.2.c.e 4
361.2.c.f 4
361.2.c.g 4
361.2.c.h 6
361.2.c.i 6
361.2.c.j 8
361.2.e \(\chi_{361}(28, \cdot)\) 361.2.e.a 6 6
361.2.e.b 6
361.2.e.c 6
361.2.e.d 6
361.2.e.e 6
361.2.e.f 6
361.2.e.g 6
361.2.e.h 6
361.2.e.i 12
361.2.e.j 12
361.2.e.k 12
361.2.e.l 12
361.2.e.m 24
361.2.g \(\chi_{361}(20, \cdot)\) 361.2.g.a 540 18
361.2.i \(\chi_{361}(7, \cdot)\) 361.2.i.a 1080 36
361.2.k \(\chi_{361}(4, \cdot)\) 361.2.k.a 3348 108

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(361))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(361)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)