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Properties

Label 365.2
Level 365
Weight 2
Dimension 4667
Nonzero newspaces 24
Newform subspaces 31
Sturm bound 21312
Trace bound 5

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Defining parameters

Level: \( N \) = \( 365 = 5 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 31 \)
Sturm bound: \(21312\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(365))\).

Total New Old
Modular forms 5616 5095 521
Cusp forms 5041 4667 374
Eisenstein series 575 428 147

Trace form

\( 4667 q - 75 q^{2} - 76 q^{3} - 79 q^{4} - 109 q^{5} - 228 q^{6} - 80 q^{7} - 87 q^{8} - 85 q^{9} + O(q^{10}) \) \( 4667 q - 75 q^{2} - 76 q^{3} - 79 q^{4} - 109 q^{5} - 228 q^{6} - 80 q^{7} - 87 q^{8} - 85 q^{9} - 111 q^{10} - 228 q^{11} - 100 q^{12} - 86 q^{13} - 96 q^{14} - 112 q^{15} - 247 q^{16} - 90 q^{17} - 111 q^{18} - 92 q^{19} - 115 q^{20} - 248 q^{21} - 108 q^{22} - 96 q^{23} - 132 q^{24} - 109 q^{25} - 258 q^{26} - 112 q^{27} - 128 q^{28} - 102 q^{29} - 120 q^{30} - 248 q^{31} - 135 q^{32} - 120 q^{33} - 126 q^{34} - 116 q^{35} - 307 q^{36} - 110 q^{37} - 132 q^{38} - 128 q^{39} - 123 q^{40} - 258 q^{41} - 168 q^{42} - 116 q^{43} - 156 q^{44} - 121 q^{45} - 288 q^{46} - 120 q^{47} - 196 q^{48} - 129 q^{49} - 111 q^{50} - 288 q^{51} - 170 q^{52} - 126 q^{53} - 192 q^{54} - 120 q^{55} - 336 q^{56} - 128 q^{57} + 18 q^{58} - 60 q^{59} + 80 q^{60} - 134 q^{61} - 24 q^{62} + 184 q^{63} + 329 q^{64} - 14 q^{65} - 72 q^{66} + 172 q^{67} + 342 q^{68} - 24 q^{69} + 156 q^{70} - 72 q^{71} + 453 q^{72} + 143 q^{73} + 30 q^{74} + 32 q^{75} + 292 q^{76} + 48 q^{77} + 336 q^{78} - 8 q^{79} + 131 q^{80} - 25 q^{81} + 90 q^{82} + 60 q^{83} + 232 q^{84} + 54 q^{85} - 204 q^{86} - 48 q^{87} + 180 q^{88} - 90 q^{89} - 57 q^{90} - 304 q^{91} - 240 q^{92} - 200 q^{93} - 216 q^{94} - 128 q^{95} - 468 q^{96} - 170 q^{97} - 243 q^{98} - 228 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(365))\)

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
365.2.a \(\chi_{365}(1, \cdot)\) 365.2.a.a 2 1
365.2.a.b 3
365.2.a.c 5
365.2.a.d 7
365.2.a.e 8
365.2.b \(\chi_{365}(74, \cdot)\) 365.2.b.a 36 1
365.2.c \(\chi_{365}(364, \cdot)\) 365.2.c.a 36 1
365.2.d \(\chi_{365}(291, \cdot)\) 365.2.d.a 26 1
365.2.e \(\chi_{365}(81, \cdot)\) 365.2.e.a 26 2
365.2.e.b 26
365.2.f \(\chi_{365}(119, \cdot)\) 365.2.f.a 68 2
365.2.k \(\chi_{365}(46, \cdot)\) 365.2.k.a 52 2
365.2.l \(\chi_{365}(211, \cdot)\) 365.2.l.a 4 2
365.2.l.b 48
365.2.m \(\chi_{365}(64, \cdot)\) 365.2.m.a 72 2
365.2.n \(\chi_{365}(9, \cdot)\) 365.2.n.a 72 2
365.2.p \(\chi_{365}(168, \cdot)\) 365.2.p.a 140 4
365.2.q \(\chi_{365}(22, \cdot)\) 365.2.q.a 140 4
365.2.s \(\chi_{365}(16, \cdot)\) 365.2.s.a 72 6
365.2.s.b 72
365.2.t \(\chi_{365}(76, \cdot)\) 365.2.t.a 104 4
365.2.y \(\chi_{365}(24, \cdot)\) 365.2.y.a 136 4
365.2.z \(\chi_{365}(36, \cdot)\) 365.2.z.a 144 6
365.2.ba \(\chi_{365}(69, \cdot)\) 365.2.ba.a 216 6
365.2.bb \(\chi_{365}(4, \cdot)\) 365.2.bb.a 216 6
365.2.bd \(\chi_{365}(7, \cdot)\) 365.2.bd.a 280 8
365.2.be \(\chi_{365}(52, \cdot)\) 365.2.be.a 280 8
365.2.bg \(\chi_{365}(19, \cdot)\) 365.2.bg.a 408 12
365.2.bl \(\chi_{365}(6, \cdot)\) 365.2.bl.a 288 12
365.2.bm \(\chi_{365}(28, \cdot)\) 365.2.bm.a 840 24
365.2.bp \(\chi_{365}(13, \cdot)\) 365.2.bp.a 840 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(365))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(365)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(73))\)\(^{\oplus 2}\)