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Properties

Label 165.4
Level 165
Weight 4
Dimension 1892
Nonzero newspaces 12
Newform subspaces 26
Sturm bound 7680
Trace bound 1

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Defining parameters

Level: \( N \) = \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 26 \)
Sturm bound: \(7680\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(165))\).

Total New Old
Modular forms 3040 1996 1044
Cusp forms 2720 1892 828
Eisenstein series 320 104 216

Trace form

\( 1892 q - 8 q^{2} + 2 q^{3} + 28 q^{4} - 12 q^{5} - 130 q^{6} - 20 q^{7} + 232 q^{8} + 186 q^{9} + O(q^{10}) \) \( 1892 q - 8 q^{2} + 2 q^{3} + 28 q^{4} - 12 q^{5} - 130 q^{6} - 20 q^{7} + 232 q^{8} + 186 q^{9} + 352 q^{10} + 256 q^{11} + 84 q^{12} - 268 q^{13} - 1308 q^{14} - 673 q^{15} - 2188 q^{16} - 680 q^{17} + 118 q^{18} + 1392 q^{19} + 1822 q^{20} + 1976 q^{21} + 3020 q^{22} + 1336 q^{23} + 2586 q^{24} + 158 q^{25} - 364 q^{26} - 1474 q^{27} - 3512 q^{28} - 2976 q^{29} - 4182 q^{30} - 4084 q^{31} - 3792 q^{32} - 3608 q^{33} - 2664 q^{34} - 120 q^{35} - 1078 q^{36} + 2580 q^{37} + 2084 q^{38} + 3378 q^{39} + 4364 q^{40} + 5168 q^{41} + 8364 q^{42} + 5616 q^{43} + 9772 q^{44} + 2388 q^{45} + 5616 q^{46} + 2136 q^{47} + 3760 q^{48} - 1160 q^{49} - 2818 q^{50} - 412 q^{51} - 10888 q^{52} - 7104 q^{53} - 648 q^{54} - 10046 q^{55} - 17360 q^{56} - 7532 q^{57} - 10192 q^{58} - 3032 q^{59} - 8202 q^{60} - 6532 q^{61} - 5824 q^{62} - 10334 q^{63} - 2948 q^{64} + 1984 q^{65} - 9376 q^{66} + 5272 q^{67} + 10416 q^{68} - 688 q^{69} + 12860 q^{70} - 2344 q^{71} + 4448 q^{72} - 4980 q^{73} + 2852 q^{74} + 7407 q^{75} + 15760 q^{76} + 3528 q^{77} + 16560 q^{78} + 10220 q^{79} + 7802 q^{80} + 14062 q^{81} + 17676 q^{82} + 12704 q^{83} + 19428 q^{84} + 4186 q^{85} + 3152 q^{86} + 11932 q^{87} + 20356 q^{88} + 8752 q^{89} + 6192 q^{90} + 10996 q^{91} + 15188 q^{92} + 3442 q^{93} + 3728 q^{94} + 5952 q^{95} - 13736 q^{96} - 5648 q^{97} - 808 q^{98} - 10558 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(165))\)

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
165.4.a \(\chi_{165}(1, \cdot)\) 165.4.a.a 1 1
165.4.a.b 1
165.4.a.c 2
165.4.a.d 3
165.4.a.e 3
165.4.a.f 3
165.4.a.g 3
165.4.a.h 4
165.4.c \(\chi_{165}(34, \cdot)\) 165.4.c.a 14 1
165.4.c.b 14
165.4.d \(\chi_{165}(164, \cdot)\) 165.4.d.a 2 1
165.4.d.b 2
165.4.d.c 64
165.4.f \(\chi_{165}(131, \cdot)\) 165.4.f.a 48 1
165.4.j \(\chi_{165}(43, \cdot)\) 165.4.j.a 72 2
165.4.k \(\chi_{165}(23, \cdot)\) 165.4.k.a 60 2
165.4.k.b 60
165.4.m \(\chi_{165}(16, \cdot)\) 165.4.m.a 24 4
165.4.m.b 24
165.4.m.c 24
165.4.m.d 24
165.4.p \(\chi_{165}(41, \cdot)\) 165.4.p.a 192 4
165.4.r \(\chi_{165}(29, \cdot)\) 165.4.r.a 272 4
165.4.s \(\chi_{165}(4, \cdot)\) 165.4.s.a 144 4
165.4.v \(\chi_{165}(38, \cdot)\) 165.4.v.a 544 8
165.4.w \(\chi_{165}(7, \cdot)\) 165.4.w.a 288 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(165))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(165)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)