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Properties

Label 168.5
Level 168
Weight 5
Dimension 1220
Nonzero newspaces 12
Sturm bound 7680
Trace bound 3

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Defining parameters

Level: \( N \) = \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(7680\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(168))\).

Total New Old
Modular forms 3216 1260 1956
Cusp forms 2928 1220 1708
Eisenstein series 288 40 248

Trace form

\( 1220 q + 12 q^{2} + 2 q^{3} - 52 q^{4} - 74 q^{6} - 32 q^{7} + 360 q^{8} - 592 q^{9} + O(q^{10}) \) \( 1220 q + 12 q^{2} + 2 q^{3} - 52 q^{4} - 74 q^{6} - 32 q^{7} + 360 q^{8} - 592 q^{9} + 652 q^{10} + 48 q^{11} - 326 q^{12} + 496 q^{13} - 420 q^{14} + 780 q^{15} + 1716 q^{16} - 1344 q^{17} + 782 q^{18} + 2100 q^{19} + 1932 q^{20} - 384 q^{21} - 5084 q^{22} - 4320 q^{23} - 6130 q^{24} + 588 q^{25} - 5076 q^{26} + 3080 q^{27} + 4548 q^{28} + 2402 q^{30} + 972 q^{31} + 4452 q^{32} - 700 q^{33} - 508 q^{34} + 6912 q^{35} + 4560 q^{36} + 2496 q^{37} - 5100 q^{38} + 4920 q^{39} + 3320 q^{40} - 1440 q^{41} + 302 q^{42} - 1480 q^{43} - 3984 q^{44} + 3400 q^{45} + 16120 q^{46} - 17280 q^{47} + 7206 q^{48} + 14628 q^{49} + 20712 q^{50} - 19646 q^{51} + 2608 q^{52} - 7344 q^{53} - 20566 q^{54} - 30584 q^{55} - 16836 q^{56} + 1032 q^{57} - 42408 q^{58} + 17376 q^{59} - 21288 q^{60} + 18112 q^{61} - 39252 q^{62} + 32270 q^{63} + 43580 q^{64} + 29904 q^{65} + 60558 q^{66} + 47364 q^{67} + 36972 q^{68} - 14512 q^{69} + 70460 q^{70} - 50400 q^{71} - 8692 q^{72} + 5120 q^{73} - 34800 q^{74} - 34724 q^{75} - 101436 q^{76} - 25920 q^{77} - 55552 q^{78} - 2676 q^{79} - 57024 q^{80} - 3720 q^{81} - 72372 q^{82} + 48000 q^{83} + 7982 q^{84} + 42368 q^{85} + 68688 q^{86} + 31476 q^{87} + 145108 q^{88} - 9312 q^{89} + 38600 q^{90} + 22296 q^{91} + 55836 q^{92} + 43480 q^{93} - 31908 q^{94} - 58176 q^{95} - 143446 q^{96} - 44080 q^{97} - 3888 q^{98} - 53132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(168))\)

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
168.5.d \(\chi_{168}(113, \cdot)\) 168.5.d.a 24 1
168.5.e \(\chi_{168}(83, \cdot)\) n/a 124 1
168.5.f \(\chi_{168}(97, \cdot)\) 168.5.f.a 16 1
168.5.g \(\chi_{168}(43, \cdot)\) 168.5.g.a 48 1
168.5.l \(\chi_{168}(13, \cdot)\) 168.5.l.a 64 1
168.5.m \(\chi_{168}(127, \cdot)\) None 0 1
168.5.n \(\chi_{168}(29, \cdot)\) 168.5.n.a 96 1
168.5.o \(\chi_{168}(167, \cdot)\) None 0 1
168.5.r \(\chi_{168}(47, \cdot)\) None 0 2
168.5.s \(\chi_{168}(53, \cdot)\) n/a 248 2
168.5.w \(\chi_{168}(79, \cdot)\) None 0 2
168.5.x \(\chi_{168}(61, \cdot)\) n/a 128 2
168.5.y \(\chi_{168}(67, \cdot)\) n/a 128 2
168.5.z \(\chi_{168}(73, \cdot)\) 168.5.z.a 16 2
168.5.z.b 16
168.5.be \(\chi_{168}(59, \cdot)\) n/a 248 2
168.5.bf \(\chi_{168}(65, \cdot)\) 168.5.bf.a 64 2

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(168))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(168)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 1}\)