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Properties

Label 366.2
Level 366
Weight 2
Dimension 931
Nonzero newspaces 12
Newform subspaces 35
Sturm bound 14880
Trace bound 2

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Defining parameters

Level: \( N \) = \( 366 = 2 \cdot 3 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 35 \)
Sturm bound: \(14880\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(366))\).

Total New Old
Modular forms 3960 931 3029
Cusp forms 3481 931 2550
Eisenstein series 479 0 479

Trace form

\( 931 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 931 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} + 6 q^{20} + 8 q^{21} + 12 q^{22} + 24 q^{23} + q^{24} + 31 q^{25} + 14 q^{26} + q^{27} + 8 q^{28} + 30 q^{29} + 6 q^{30} + 32 q^{31} + q^{32} + 12 q^{33} + 18 q^{34} + 48 q^{35} + q^{36} + 38 q^{37} + 20 q^{38} + 14 q^{39} + 6 q^{40} + 42 q^{41} + 8 q^{42} + 44 q^{43} + 12 q^{44} + 6 q^{45} + 24 q^{46} - 72 q^{47} - 19 q^{48} - 223 q^{49} - 119 q^{50} - 102 q^{51} - 136 q^{52} - 66 q^{53} + q^{54} - 408 q^{55} - 112 q^{56} - 220 q^{57} - 210 q^{58} - 180 q^{59} + 6 q^{60} - 459 q^{61} - 328 q^{62} - 12 q^{63} + q^{64} - 156 q^{65} - 108 q^{66} - 412 q^{67} - 102 q^{68} - 216 q^{69} - 312 q^{70} - 48 q^{71} - 29 q^{72} - 166 q^{73} - 112 q^{74} - 109 q^{75} - 20 q^{76} - 24 q^{77} + 14 q^{78} + 80 q^{79} + 6 q^{80} + q^{81} + 42 q^{82} + 84 q^{83} + 8 q^{84} + 108 q^{85} + 44 q^{86} + 30 q^{87} + 12 q^{88} + 90 q^{89} + 6 q^{90} + 112 q^{91} + 24 q^{92} + 32 q^{93} + 48 q^{94} + 120 q^{95} + q^{96} + 98 q^{97} + 57 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(366))\)

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
366.2.a \(\chi_{366}(1, \cdot)\) 366.2.a.a 1 1
366.2.a.b 1
366.2.a.c 1
366.2.a.d 1
366.2.a.e 1
366.2.a.f 1
366.2.a.g 1
366.2.a.h 2
366.2.d \(\chi_{366}(121, \cdot)\) 366.2.d.a 4 1
366.2.d.b 6
366.2.e \(\chi_{366}(13, \cdot)\) 366.2.e.a 2 2
366.2.e.b 2
366.2.e.c 4
366.2.e.d 6
366.2.e.e 6
366.2.g \(\chi_{366}(11, \cdot)\) 366.2.g.a 4 2
366.2.g.b 40
366.2.h \(\chi_{366}(217, \cdot)\) 366.2.h.a 4 4
366.2.h.b 8
366.2.h.c 8
366.2.h.d 12
366.2.i \(\chi_{366}(109, \cdot)\) 366.2.i.a 12 2
366.2.i.b 12
366.2.l \(\chi_{366}(163, \cdot)\) 366.2.l.a 8 4
366.2.l.b 8
366.2.l.c 24
366.2.o \(\chi_{366}(29, \cdot)\) 366.2.o.a 80 4
366.2.q \(\chi_{366}(25, \cdot)\) 366.2.q.a 16 8
366.2.q.b 16
366.2.q.c 24
366.2.q.d 24
366.2.r \(\chi_{366}(23, \cdot)\) 366.2.r.a 176 8
366.2.v \(\chi_{366}(19, \cdot)\) 366.2.v.a 48 8
366.2.v.b 48
366.2.x \(\chi_{366}(17, \cdot)\) 366.2.x.a 320 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(366))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(366)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)\(^{\oplus 2}\)