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Properties

Label 70.10
Level 70
Weight 10
Dimension 382
Nonzero newspaces 6
Newform subspaces 18
Sturm bound 2880
Trace bound 4

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Defining parameters

Level: \( N \) = \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 18 \)
Sturm bound: \(2880\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(70))\).

Total New Old
Modular forms 1344 382 962
Cusp forms 1248 382 866
Eisenstein series 96 0 96

Trace form

\( 382 q + 32 q^{2} + 616 q^{3} + 512 q^{4} + 8114 q^{5} - 16448 q^{6} + 5700 q^{7} + 8192 q^{8} + 12638 q^{9} + O(q^{10}) \) \( 382 q + 32 q^{2} + 616 q^{3} + 512 q^{4} + 8114 q^{5} - 16448 q^{6} + 5700 q^{7} + 8192 q^{8} + 12638 q^{9} - 166976 q^{10} + 138132 q^{11} + 157696 q^{12} - 655248 q^{13} + 44480 q^{14} - 1111412 q^{15} - 917504 q^{16} + 5202504 q^{17} + 1201184 q^{18} - 6425040 q^{19} - 1960960 q^{20} + 5206328 q^{21} + 3302400 q^{22} + 7558788 q^{23} - 1720320 q^{24} - 13780308 q^{25} + 1514752 q^{26} - 994736 q^{27} + 5388288 q^{28} - 1116612 q^{29} - 30147456 q^{30} - 35034404 q^{31} + 2097152 q^{32} + 35704092 q^{33} + 46193600 q^{34} + 31843160 q^{35} - 102369792 q^{36} + 8392608 q^{37} + 36918592 q^{38} - 92368840 q^{39} + 13615104 q^{40} - 175863276 q^{41} + 129196736 q^{42} + 353229144 q^{43} - 47619072 q^{44} - 110642700 q^{45} - 160226432 q^{46} + 120152988 q^{47} - 23330816 q^{48} - 187625770 q^{49} + 147790304 q^{50} + 113841764 q^{51} + 11335680 q^{52} - 515912424 q^{53} - 519383424 q^{54} - 259817188 q^{55} - 41304064 q^{56} + 118232384 q^{57} + 417960768 q^{58} - 306017832 q^{59} + 387503616 q^{60} + 675675092 q^{61} - 290685056 q^{62} - 1647508796 q^{63} - 570425344 q^{64} - 1873488596 q^{65} - 309862400 q^{66} + 938958228 q^{67} + 1331841024 q^{68} + 6644471944 q^{69} + 1278798048 q^{70} - 1283637216 q^{71} + 307503104 q^{72} - 4512995568 q^{73} - 3246990272 q^{74} - 4125038614 q^{75} - 25347072 q^{76} + 327355260 q^{77} + 1198949632 q^{78} + 3022543404 q^{79} + 531759104 q^{80} + 5852382066 q^{81} + 1032087744 q^{82} + 569376396 q^{83} + 1280225280 q^{84} - 5530868524 q^{85} - 850212224 q^{86} - 4083130440 q^{87} - 1953792000 q^{88} - 2569404240 q^{89} + 4627946688 q^{90} + 7212029220 q^{91} - 240402432 q^{92} + 6428170028 q^{93} - 1287790976 q^{94} - 9637356494 q^{95} - 952107008 q^{96} - 880551852 q^{97} - 3963965920 q^{98} - 6716889232 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(70))\)

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
70.10.a \(\chi_{70}(1, \cdot)\) 70.10.a.a 1 1
70.10.a.b 1
70.10.a.c 2
70.10.a.d 2
70.10.a.e 2
70.10.a.f 2
70.10.a.g 2
70.10.a.h 3
70.10.a.i 3
70.10.c \(\chi_{70}(29, \cdot)\) 70.10.c.a 12 1
70.10.c.b 16
70.10.e \(\chi_{70}(11, \cdot)\) 70.10.e.a 10 2
70.10.e.b 12
70.10.e.c 12
70.10.e.d 14
70.10.g \(\chi_{70}(13, \cdot)\) 70.10.g.a 72 2
70.10.i \(\chi_{70}(9, \cdot)\) 70.10.i.a 72 2
70.10.k \(\chi_{70}(3, \cdot)\) 70.10.k.a 144 4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(70))\) into lower level spaces

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