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Properties

Label 162.13
Level 162
Weight 13
Dimension 2304
Nonzero newspaces 4
Sturm bound 18954
Trace bound 1

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Defining parameters

Level: \( N \) = \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) = \( 13 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(18954\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(162))\).

Total New Old
Modular forms 8856 2304 6552
Cusp forms 8640 2304 6336
Eisenstein series 216 0 216

Trace form

\( 2304 q + 31968 q^{5} + 205920 q^{7} + O(q^{10}) \) \( 2304 q + 31968 q^{5} + 205920 q^{7} + 1317888 q^{10} + 7514316 q^{11} + 4189680 q^{13} + 19920384 q^{14} - 174343680 q^{18} + 402987960 q^{19} - 327352320 q^{20} - 721401120 q^{21} + 471340800 q^{22} + 1370064240 q^{23} - 1438498656 q^{25} + 3702741120 q^{27} + 1686896640 q^{28} - 1941418584 q^{29} - 7522454016 q^{30} - 5777639280 q^{31} + 15309302400 q^{33} + 2025100800 q^{34} - 41951302272 q^{35} - 8009809920 q^{36} + 22870529640 q^{37} - 13206723840 q^{38} - 2699034624 q^{40} - 51347535012 q^{41} + 37109579220 q^{43} - 81805475232 q^{45} - 16593325056 q^{46} + 90767579400 q^{47} + 108202079952 q^{49} + 30185561088 q^{50} - 155737952244 q^{51} - 8580464640 q^{52} + 270411498144 q^{55} + 40796946432 q^{56} - 19236737520 q^{57} - 79719575040 q^{58} - 427367457180 q^{59} + 182608903224 q^{61} + 519250909320 q^{63} - 309237645312 q^{64} + 6156270432 q^{65} - 150488432640 q^{66} + 765466666020 q^{67} + 152276336640 q^{68} + 1796976637632 q^{69} - 640710111744 q^{70} + 594921697920 q^{71} - 512816578560 q^{72} - 413936160120 q^{73} - 1848413274624 q^{74} - 1406250000000 q^{75} + 48727203840 q^{76} + 4858820223120 q^{77} + 3615067607040 q^{78} - 1205218723464 q^{79} - 2799877893120 q^{81} + 179924797440 q^{82} - 5013155930760 q^{83} - 680036696064 q^{84} + 176128158024 q^{85} + 4208891321088 q^{86} + 14377253184000 q^{87} - 965305958400 q^{88} + 127647209880 q^{89} - 3505536000000 q^{90} - 1715839267680 q^{91} - 4511932416000 q^{92} - 6269441677560 q^{93} - 37361834496 q^{94} + 6480820477944 q^{95} + 2222645575680 q^{96} + 2151268165260 q^{97} - 6989014056960 q^{98} - 5192452549728 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(162))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
162.13.b \(\chi_{162}(161, \cdot)\) 162.13.b.a 12 1
162.13.b.b 12
162.13.b.c 24
162.13.d \(\chi_{162}(53, \cdot)\) 162.13.d.a 4 2
162.13.d.b 4
162.13.d.c 8
162.13.d.d 8
162.13.d.e 8
162.13.d.f 16
162.13.d.g 24
162.13.d.h 24
162.13.f \(\chi_{162}(17, \cdot)\) n/a 216 6
162.13.h \(\chi_{162}(5, \cdot)\) n/a 1944 18

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

Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

\( S_{13}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)