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Properties

Label 162.7
Level 162
Weight 7
Dimension 1152
Nonzero newspaces 4
Sturm bound 10206
Trace bound 1

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Defining parameters

Level: \( N \) = \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(10206\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(162))\).

Total New Old
Modular forms 4482 1152 3330
Cusp forms 4266 1152 3114
Eisenstein series 216 0 216

Trace form

\( 1152 q + 432 q^{5} - 720 q^{7} + O(q^{10}) \) \( 1152 q + 432 q^{5} - 720 q^{7} + 1872 q^{10} + 378 q^{11} - 3384 q^{13} - 4752 q^{14} + 33120 q^{18} - 30780 q^{19} - 69120 q^{20} - 41040 q^{21} + 25200 q^{22} + 195912 q^{23} + 54000 q^{25} - 112320 q^{27} - 92160 q^{28} - 408348 q^{29} - 223776 q^{30} - 113400 q^{31} + 302400 q^{33} + 199440 q^{34} + 1073088 q^{35} + 92160 q^{36} - 116892 q^{37} - 589248 q^{38} - 59904 q^{40} + 523854 q^{41} - 541674 q^{43} - 582768 q^{45} + 135072 q^{46} + 1096092 q^{47} + 871704 q^{49} + 311040 q^{50} + 882378 q^{51} + 108288 q^{52} - 1682640 q^{55} - 152064 q^{56} - 1372680 q^{57} - 222768 q^{58} - 2081970 q^{59} + 117612 q^{61} + 1778220 q^{63} - 589824 q^{64} + 1875744 q^{65} + 262080 q^{66} - 927234 q^{67} + 1237248 q^{68} + 4444704 q^{69} - 1259856 q^{70} + 855360 q^{71} - 700416 q^{72} - 1885212 q^{73} - 5250528 q^{74} - 9000000 q^{75} + 745920 q^{76} - 6680664 q^{77} - 4901760 q^{78} + 3177972 q^{79} + 2787840 q^{81} - 167040 q^{82} + 4233060 q^{83} + 2310912 q^{84} - 5279580 q^{85} + 8059824 q^{86} + 16240896 q^{87} - 806400 q^{88} + 5545260 q^{89} - 2448000 q^{90} - 1835280 q^{91} - 5405184 q^{92} - 17804268 q^{93} + 3166128 q^{94} - 19467324 q^{95} - 1474560 q^{96} - 1542330 q^{97} + 4393440 q^{98} + 26461584 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(162))\)

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
162.7.b \(\chi_{162}(161, \cdot)\) 162.7.b.a 4 1
162.7.b.b 8
162.7.b.c 12
162.7.d \(\chi_{162}(53, \cdot)\) 162.7.d.a 4 2
162.7.d.b 4
162.7.d.c 4
162.7.d.d 4
162.7.d.e 8
162.7.d.f 8
162.7.d.g 16
162.7.f \(\chi_{162}(17, \cdot)\) n/a 108 6
162.7.h \(\chi_{162}(5, \cdot)\) n/a 972 18

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 1}\)