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Properties

Label 168.10
Level 168
Weight 10
Dimension 2778
Nonzero newspaces 12
Sturm bound 15360
Trace bound 3

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Defining parameters

Level: \( N \) = \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(15360\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(168))\).

Total New Old
Modular forms 7056 2818 4238
Cusp forms 6768 2778 3990
Eisenstein series 288 40 248

Trace form

\( 2778 q - 68 q^{2} + 160 q^{3} - 1716 q^{4} + 244 q^{5} + 7318 q^{6} + 15496 q^{7} - 31688 q^{8} + 221272 q^{9} + O(q^{10}) \) \( 2778 q - 68 q^{2} + 160 q^{3} - 1716 q^{4} + 244 q^{5} + 7318 q^{6} + 15496 q^{7} - 31688 q^{8} + 221272 q^{9} + 82668 q^{10} - 56924 q^{11} - 1142 q^{12} - 164896 q^{13} + 209204 q^{14} - 808524 q^{15} - 1640524 q^{16} - 1327616 q^{17} + 3085006 q^{18} + 4479060 q^{19} + 1348636 q^{20} - 3780768 q^{21} - 11907276 q^{22} + 10404636 q^{23} + 10287022 q^{24} - 6792162 q^{25} - 1897076 q^{26} + 10524316 q^{27} - 39158620 q^{28} + 1473636 q^{29} + 43775010 q^{30} + 37264972 q^{31} + 987572 q^{32} - 22505890 q^{33} - 45910940 q^{34} - 35053572 q^{35} + 15939136 q^{36} - 13669800 q^{37} - 16817692 q^{38} + 26360940 q^{39} - 207220504 q^{40} + 256564 q^{41} + 96148950 q^{42} + 84085168 q^{43} - 32815248 q^{44} + 64813530 q^{45} + 19675064 q^{46} - 268245336 q^{47} - 93199610 q^{48} - 311389822 q^{49} - 76654808 q^{50} + 110923520 q^{51} + 426055088 q^{52} + 152477488 q^{53} + 411280090 q^{54} - 1070894756 q^{55} + 333253244 q^{56} - 201595648 q^{57} + 458151832 q^{58} + 1174608112 q^{59} - 844198224 q^{60} + 161437748 q^{61} - 1444483012 q^{62} - 165286560 q^{63} - 201031332 q^{64} - 1418049448 q^{65} + 1546837358 q^{66} + 686315820 q^{67} - 355704084 q^{68} + 216857736 q^{69} - 1830766420 q^{70} - 68797120 q^{71} + 2971439668 q^{72} - 3450029692 q^{73} + 957942112 q^{74} + 350006356 q^{75} - 2863481052 q^{76} + 503010852 q^{77} - 1121838720 q^{78} + 1827877804 q^{79} + 1333989888 q^{80} - 2302778288 q^{81} - 789429780 q^{82} - 3780229768 q^{83} + 4495339230 q^{84} + 1348207408 q^{85} + 2870000560 q^{86} + 3388760208 q^{87} + 1671115668 q^{88} + 3748148668 q^{89} - 6571905984 q^{90} - 2089905024 q^{91} - 2617662948 q^{92} - 3014359038 q^{93} - 5989346820 q^{94} - 9785956088 q^{95} + 13686592090 q^{96} - 9274343152 q^{97} + 7501562368 q^{98} + 39901304 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(168))\)

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
168.10.a \(\chi_{168}(1, \cdot)\) 168.10.a.a 3 1
168.10.a.b 3
168.10.a.c 3
168.10.a.d 3
168.10.a.e 3
168.10.a.f 3
168.10.a.g 4
168.10.a.h 4
168.10.b \(\chi_{168}(55, \cdot)\) None 0 1
168.10.c \(\chi_{168}(85, \cdot)\) n/a 108 1
168.10.h \(\chi_{168}(71, \cdot)\) None 0 1
168.10.i \(\chi_{168}(125, \cdot)\) n/a 284 1
168.10.j \(\chi_{168}(155, \cdot)\) n/a 216 1
168.10.k \(\chi_{168}(41, \cdot)\) 168.10.k.a 72 1
168.10.p \(\chi_{168}(139, \cdot)\) n/a 144 1
168.10.q \(\chi_{168}(25, \cdot)\) 168.10.q.a 16 2
168.10.q.b 18
168.10.q.c 18
168.10.q.d 20
168.10.t \(\chi_{168}(19, \cdot)\) n/a 288 2
168.10.u \(\chi_{168}(17, \cdot)\) n/a 144 2
168.10.v \(\chi_{168}(11, \cdot)\) n/a 568 2
168.10.ba \(\chi_{168}(5, \cdot)\) n/a 568 2
168.10.bb \(\chi_{168}(23, \cdot)\) None 0 2
168.10.bc \(\chi_{168}(37, \cdot)\) n/a 288 2
168.10.bd \(\chi_{168}(31, \cdot)\) None 0 2

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(168))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(168)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 1}\)