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Properties

Label 162.11
Level 162
Weight 11
Dimension 1920
Nonzero newspaces 4
Sturm bound 16038
Trace bound 1

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Defining parameters

Level: \( N \) = \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(16038\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(162))\).

Total New Old
Modular forms 7398 1920 5478
Cusp forms 7182 1920 5262
Eisenstein series 216 0 216

Trace form

\( 1920 q - 9918 q^{5} - 36714 q^{7} + O(q^{10}) \) \( 1920 q - 9918 q^{5} - 36714 q^{7} - 15168 q^{10} - 327582 q^{11} + 1132986 q^{13} + 175680 q^{14} - 3053952 q^{18} + 4914900 q^{19} + 25390080 q^{20} - 28173150 q^{21} - 24314304 q^{22} + 4419882 q^{23} + 72403110 q^{25} - 123046506 q^{27} - 75190272 q^{28} - 101811510 q^{29} + 144526464 q^{30} + 258107274 q^{31} - 122955462 q^{33} - 145246272 q^{34} - 1040614452 q^{35} + 135705600 q^{36} + 706583352 q^{37} - 371467008 q^{38} + 7766016 q^{40} - 1015759638 q^{41} + 171163458 q^{43} + 194789232 q^{45} + 366913920 q^{46} - 2855909718 q^{47} + 321223038 q^{49} - 456606720 q^{50} + 3031812630 q^{51} - 580088832 q^{52} - 1939653900 q^{55} + 89948160 q^{56} - 1983447864 q^{57} - 1782781248 q^{58} + 7619146290 q^{59} + 2476595718 q^{61} - 4406834700 q^{63} - 4026531840 q^{64} + 1261214514 q^{65} + 17916772608 q^{66} + 7883026470 q^{67} - 4824235008 q^{68} - 34587102960 q^{69} - 2684043456 q^{70} + 11025824328 q^{71} + 18258591744 q^{72} + 9509547678 q^{73} + 17211348864 q^{74} - 10898437500 q^{75} + 4916416512 q^{76} - 78274940886 q^{77} - 42945311232 q^{78} + 19069600818 q^{79} + 29482836336 q^{81} + 5172896256 q^{82} + 48191439402 q^{83} + 13610373120 q^{84} - 36515383560 q^{85} - 17381635776 q^{86} - 107586841824 q^{87} + 12448923648 q^{88} - 55146217014 q^{89} - 70488000000 q^{90} + 8381777430 q^{91} + 19851807744 q^{92} + 144353719260 q^{93} - 61144125120 q^{94} + 64386743436 q^{95} - 3321888768 q^{96} + 9109842078 q^{97} - 72176531328 q^{98} - 18892680552 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(162))\)

We only show spaces with odd 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
162.11.b \(\chi_{162}(161, \cdot)\) 162.11.b.a 8 1
162.11.b.b 12
162.11.b.c 20
162.11.d \(\chi_{162}(53, \cdot)\) 162.11.d.a 4 2
162.11.d.b 4
162.11.d.c 8
162.11.d.d 8
162.11.d.e 16
162.11.d.f 16
162.11.d.g 24
162.11.f \(\chi_{162}(17, \cdot)\) n/a 180 6
162.11.h \(\chi_{162}(5, \cdot)\) n/a 1620 18

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

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)