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Properties

Label 70.5
Level 70
Weight 5
Dimension 168
Nonzero newspaces 6
Newform subspaces 8
Sturm bound 1440
Trace bound 3

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Defining parameters

Level: \( N \) = \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
Sturm bound: \(1440\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(70))\).

Total New Old
Modular forms 624 168 456
Cusp forms 528 168 360
Eisenstein series 96 0 96

Trace form

\( 168 q - 4 q^{3} - 32 q^{4} + 66 q^{5} + 128 q^{6} + 188 q^{7} + 336 q^{9} + O(q^{10}) \) \( 168 q - 4 q^{3} - 32 q^{4} + 66 q^{5} + 128 q^{6} + 188 q^{7} + 336 q^{9} - 224 q^{10} - 948 q^{11} - 608 q^{12} + 120 q^{13} + 576 q^{14} + 284 q^{15} + 256 q^{16} + 204 q^{17} - 256 q^{18} - 60 q^{19} - 1748 q^{21} - 640 q^{22} - 684 q^{23} + 1536 q^{24} - 3674 q^{25} + 3840 q^{26} + 1880 q^{27} + 1344 q^{28} - 1008 q^{29} + 5184 q^{30} + 10948 q^{31} + 9116 q^{33} - 4890 q^{35} + 128 q^{36} - 3316 q^{37} - 4800 q^{38} - 23640 q^{39} - 3328 q^{40} - 21984 q^{41} - 10432 q^{42} - 15544 q^{43} - 2016 q^{44} + 6028 q^{45} - 3200 q^{46} + 18756 q^{47} + 2560 q^{48} + 21488 q^{49} + 20544 q^{50} + 43060 q^{51} + 1728 q^{52} - 7452 q^{53} + 2880 q^{54} - 23856 q^{55} + 1536 q^{56} - 18328 q^{57} - 22400 q^{58} - 16092 q^{59} + 4016 q^{60} + 32100 q^{61} + 7680 q^{62} + 25084 q^{63} - 8192 q^{64} + 24648 q^{65} - 13312 q^{66} + 19860 q^{67} - 1632 q^{68} + 1760 q^{70} - 19632 q^{71} - 2048 q^{72} + 10348 q^{73} + 15552 q^{74} - 45494 q^{75} + 10240 q^{76} - 54204 q^{77} - 15744 q^{78} - 82820 q^{79} - 4224 q^{80} + 50452 q^{81} - 14848 q^{82} + 20760 q^{83} - 2208 q^{84} + 5996 q^{85} + 7680 q^{86} - 75088 q^{87} + 9728 q^{88} - 59652 q^{89} - 40384 q^{90} - 15816 q^{91} - 5760 q^{92} + 2012 q^{93} + 54144 q^{94} + 161778 q^{95} + 4096 q^{96} + 173160 q^{97} + 90624 q^{98} + 248160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(70))\)

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
70.5.b \(\chi_{70}(41, \cdot)\) 70.5.b.a 8 1
70.5.d \(\chi_{70}(69, \cdot)\) 70.5.d.a 16 1
70.5.f \(\chi_{70}(43, \cdot)\) 70.5.f.a 12 2
70.5.f.b 12
70.5.h \(\chi_{70}(19, \cdot)\) 70.5.h.a 32 2
70.5.j \(\chi_{70}(31, \cdot)\) 70.5.j.a 24 2
70.5.l \(\chi_{70}(23, \cdot)\) 70.5.l.a 32 4
70.5.l.b 32

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(70))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(70)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)