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Properties

Label 165.6
Level 165
Weight 6
Dimension 3192
Nonzero newspaces 12
Sturm bound 11520
Trace bound 1

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Defining parameters

Level: \( N \) = \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(11520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(165))\).

Total New Old
Modular forms 4960 3296 1664
Cusp forms 4640 3192 1448
Eisenstein series 320 104 216

Trace form

\( 3192 q - 8 q^{2} + 26 q^{3} - 196 q^{4} - 240 q^{5} + 242 q^{6} + 1784 q^{7} + 1096 q^{8} - 1110 q^{9} + O(q^{10}) \) \( 3192 q - 8 q^{2} + 26 q^{3} - 196 q^{4} - 240 q^{5} + 242 q^{6} + 1784 q^{7} + 1096 q^{8} - 1110 q^{9} - 5640 q^{10} - 2948 q^{11} + 228 q^{12} + 7808 q^{13} + 9972 q^{14} + 10625 q^{15} + 23060 q^{16} + 1708 q^{17} - 20678 q^{18} - 15712 q^{19} - 22130 q^{20} - 21232 q^{21} - 46852 q^{22} - 11288 q^{23} - 6726 q^{24} + 10 q^{25} + 61748 q^{26} + 8696 q^{27} + 116328 q^{28} + 15096 q^{29} + 52110 q^{30} + 14716 q^{31} - 107856 q^{32} + 13582 q^{33} + 26968 q^{34} + 12840 q^{35} - 36478 q^{36} - 34996 q^{37} - 34108 q^{38} - 72444 q^{39} - 7620 q^{40} - 115000 q^{41} + 25092 q^{42} + 31040 q^{43} - 276500 q^{44} + 25695 q^{45} - 159824 q^{46} - 152340 q^{47} - 92960 q^{48} + 99952 q^{49} + 102350 q^{50} + 122420 q^{51} + 141848 q^{52} + 366852 q^{53} + 17496 q^{54} + 252450 q^{55} + 268720 q^{56} - 171608 q^{57} + 250864 q^{58} + 193852 q^{59} + 398790 q^{60} - 12712 q^{61} - 509872 q^{62} - 103436 q^{63} - 944420 q^{64} - 560060 q^{65} + 600512 q^{66} - 62852 q^{67} + 283344 q^{68} + 135662 q^{69} + 508460 q^{70} - 446872 q^{71} - 137824 q^{72} + 52192 q^{73} + 424772 q^{74} + 379095 q^{75} + 414896 q^{76} + 488724 q^{77} - 807648 q^{78} + 279160 q^{79} - 299110 q^{80} - 53258 q^{81} - 403692 q^{82} - 499444 q^{83} - 529692 q^{84} - 517540 q^{85} - 16096 q^{86} - 132116 q^{87} - 1646172 q^{88} + 108688 q^{89} + 1637700 q^{90} + 917656 q^{91} + 943604 q^{92} + 272326 q^{93} + 564336 q^{94} - 1134510 q^{95} - 929816 q^{96} - 170732 q^{97} - 472168 q^{98} + 219554 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(165))\)

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
165.6.a \(\chi_{165}(1, \cdot)\) 165.6.a.a 3 1
165.6.a.b 3
165.6.a.c 3
165.6.a.d 3
165.6.a.e 3
165.6.a.f 5
165.6.a.g 5
165.6.a.h 7
165.6.c \(\chi_{165}(34, \cdot)\) 165.6.c.a 26 1
165.6.c.b 26
165.6.d \(\chi_{165}(164, \cdot)\) n/a 116 1
165.6.f \(\chi_{165}(131, \cdot)\) 165.6.f.a 80 1
165.6.j \(\chi_{165}(43, \cdot)\) n/a 120 2
165.6.k \(\chi_{165}(23, \cdot)\) n/a 200 2
165.6.m \(\chi_{165}(16, \cdot)\) n/a 160 4
165.6.p \(\chi_{165}(41, \cdot)\) n/a 320 4
165.6.r \(\chi_{165}(29, \cdot)\) n/a 464 4
165.6.s \(\chi_{165}(4, \cdot)\) n/a 240 4
165.6.v \(\chi_{165}(38, \cdot)\) n/a 928 8
165.6.w \(\chi_{165}(7, \cdot)\) n/a 480 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(165))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(165)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)