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Properties

Label 162.9
Level 162
Weight 9
Dimension 1536
Nonzero newspaces 4
Sturm bound 13122
Trace bound 1

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Defining parameters

Level: \( N \) = \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(13122\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(162))\).

Total New Old
Modular forms 5940 1536 4404
Cusp forms 5724 1536 4188
Eisenstein series 216 0 216

Trace form

\( 1536 q - 882 q^{5} + 5538 q^{7} + O(q^{10}) \) \( 1536 q - 882 q^{5} + 5538 q^{7} - 10752 q^{10} + 45756 q^{11} - 47010 q^{13} - 94464 q^{14} + 274176 q^{18} - 1287720 q^{19} + 564480 q^{20} + 2721870 q^{21} + 432768 q^{22} - 2417130 q^{23} - 3077046 q^{25} + 3866562 q^{27} + 2835456 q^{28} + 8563554 q^{29} + 1292544 q^{30} - 4082634 q^{31} - 12138714 q^{33} + 930048 q^{34} + 24901668 q^{35} + 9112320 q^{36} + 310452 q^{37} - 26812800 q^{38} + 1376256 q^{40} + 22128480 q^{41} + 293184 q^{43} + 37896768 q^{45} - 7417344 q^{46} + 4632930 q^{47} - 32417574 q^{49} + 27744768 q^{50} - 54355896 q^{51} + 6017280 q^{52} + 46682604 q^{55} - 12091392 q^{56} + 65747808 q^{57} + 21354240 q^{58} + 79170120 q^{59} - 72977202 q^{61} - 101958480 q^{63} - 50331648 q^{64} - 6305058 q^{65} + 297787392 q^{66} - 83055708 q^{67} + 2458368 q^{68} - 398223792 q^{69} + 181798656 q^{70} - 251437608 q^{71} - 182845440 q^{72} + 29703630 q^{73} + 112151808 q^{74} + 492187500 q^{75} - 114868992 q^{76} + 583530174 q^{77} + 478734336 q^{78} - 193129518 q^{79} - 296732016 q^{81} + 44018688 q^{82} - 254457126 q^{83} - 196816896 q^{84} + 468568404 q^{85} - 388996992 q^{86} - 122724000 q^{87} - 55394304 q^{88} + 764382906 q^{89} + 1128960000 q^{90} - 367342590 q^{91} + 432693504 q^{92} + 497955456 q^{93} + 279518976 q^{94} + 169987104 q^{95} - 264241152 q^{96} + 809887524 q^{97} - 234233856 q^{98} + 1648813176 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(162))\)

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
162.9.b \(\chi_{162}(161, \cdot)\) 162.9.b.a 8 1
162.9.b.b 8
162.9.b.c 16
162.9.d \(\chi_{162}(53, \cdot)\) 162.9.d.a 4 2
162.9.d.b 4
162.9.d.c 4
162.9.d.d 4
162.9.d.e 8
162.9.d.f 8
162.9.d.g 16
162.9.d.h 16
162.9.f \(\chi_{162}(17, \cdot)\) n/a 144 6
162.9.h \(\chi_{162}(5, \cdot)\) n/a 1296 18

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

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