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Properties

Label 162.14
Level 162
Weight 14
Dimension 2496
Nonzero newspaces 4
Sturm bound 20412
Trace bound 1

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Defining parameters

Level: \( N \) = \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(20412\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(162))\).

Total New Old
Modular forms 9585 2496 7089
Cusp forms 9369 2496 6873
Eisenstein series 216 0 216

Trace form

\( 2496 q - 125274 q^{5} - 563466 q^{7} + 786432 q^{8} + O(q^{10}) \) \( 2496 q - 125274 q^{5} - 563466 q^{7} + 786432 q^{8} - 3195264 q^{10} + 16856979 q^{11} - 27314340 q^{13} + 67302528 q^{14} + 289650828 q^{17} + 878791104 q^{18} - 1995447978 q^{19} + 2565611520 q^{20} - 1907750934 q^{21} - 2235019584 q^{22} + 5823817842 q^{23} - 606212676 q^{25} - 27802419840 q^{26} - 6570366246 q^{27} + 9231826944 q^{28} + 48887292228 q^{29} - 6189865344 q^{30} - 40256773236 q^{31} + 54121048074 q^{33} + 53194670400 q^{34} - 26459864412 q^{35} - 68850229248 q^{36} + 62021864082 q^{37} + 32819302848 q^{38} - 13087801344 q^{40} + 306031857585 q^{41} - 2896942851 q^{43} + 43537883136 q^{44} + 243594028026 q^{45} - 39735101184 q^{46} - 1277668387854 q^{47} + 286618622964 q^{49} + 636147553536 q^{50} + 283030447581 q^{51} - 111879536640 q^{52} - 3218472850350 q^{53} + 1057866004764 q^{55} + 275671154688 q^{56} + 1808232087114 q^{57} - 1169650119936 q^{58} - 3036703118289 q^{59} - 1662453994122 q^{61} + 1363205654016 q^{62} + 3670301056914 q^{63} + 2680059592704 q^{64} - 11081005713636 q^{65} + 6972068408832 q^{66} - 8721140852889 q^{67} - 433851408384 q^{68} - 17913160134162 q^{69} + 5170905700608 q^{70} + 9191104344120 q^{71} + 11318750871552 q^{72} - 6330311234382 q^{73} - 4749182661504 q^{74} - 26323242187500 q^{75} + 5870173900800 q^{76} - 26607744248154 q^{77} + 3117864692736 q^{78} - 18027296646468 q^{79} + 6291456000000 q^{80} + 30553342249104 q^{81} + 217227479424 q^{82} - 10619999333784 q^{83} - 12448074350592 q^{84} + 14666161548708 q^{85} - 27822058612416 q^{86} + 38284169253408 q^{87} - 9154640216064 q^{88} + 115826712663774 q^{89} + 53589744000000 q^{90} - 18632438542194 q^{91} - 36212178739200 q^{92} - 116692065793962 q^{93} + 5091001589376 q^{94} + 74105224995468 q^{95} + 24139863687168 q^{96} - 34877042900043 q^{97} - 58150197383232 q^{98} - 195071777635518 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(162))\)

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
162.14.a \(\chi_{162}(1, \cdot)\) 162.14.a.a 3 1
162.14.a.b 3
162.14.a.c 4
162.14.a.d 4
162.14.a.e 6
162.14.a.f 6
162.14.a.g 6
162.14.a.h 6
162.14.a.i 7
162.14.a.j 7
162.14.c \(\chi_{162}(55, \cdot)\) n/a 104 2
162.14.e \(\chi_{162}(19, \cdot)\) n/a 234 6
162.14.g \(\chi_{162}(7, \cdot)\) n/a 2106 18

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 1}\)