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Properties

Label 74.8
Level 74
Weight 8
Dimension 397
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 2736
Trace bound 1

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Defining parameters

Level: \( N \) = \( 74 = 2 \cdot 37 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(2736\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(74))\).

Total New Old
Modular forms 1233 397 836
Cusp forms 1161 397 764
Eisenstein series 72 0 72

Trace form

\( 397 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} + 192 q^{6} - 2032 q^{7} + 1024 q^{8} + 4086 q^{9} + O(q^{10}) \) \( 397 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} + 192 q^{6} - 2032 q^{7} + 1024 q^{8} + 4086 q^{9} - 3360 q^{10} - 2184 q^{11} - 1536 q^{12} - 2764 q^{13} + 16256 q^{14} + 5040 q^{15} - 8192 q^{16} - 29412 q^{17} - 32688 q^{18} + 79880 q^{19} + 26880 q^{20} - 24384 q^{21} + 17472 q^{22} - 137424 q^{23} + 12288 q^{24} + 68050 q^{25} + 814328 q^{26} - 843264 q^{27} - 516352 q^{28} - 69576 q^{29} + 1374912 q^{30} + 3120668 q^{31} + 65536 q^{32} + 710568 q^{33} - 788256 q^{34} - 3428772 q^{35} - 1838016 q^{36} - 3740858 q^{37} - 1473952 q^{38} + 617748 q^{39} + 1697280 q^{40} + 7617048 q^{41} + 6058176 q^{42} + 5979872 q^{43} - 139776 q^{44} - 6448032 q^{45} - 8097600 q^{46} - 7035180 q^{47} - 1425408 q^{48} + 6606366 q^{49} + 6120424 q^{50} - 352944 q^{51} - 176896 q^{52} + 2988036 q^{53} - 812160 q^{54} + 458640 q^{55} + 1040384 q^{56} + 958560 q^{57} - 1641120 q^{58} - 2217972 q^{59} + 322560 q^{60} - 17429389 q^{61} + 3640832 q^{62} + 2137500 q^{63} - 524288 q^{64} + 23156679 q^{65} + 209664 q^{66} + 10380860 q^{67} - 1882368 q^{68} + 4733424 q^{69} - 3413760 q^{70} - 14633640 q^{71} - 2092032 q^{72} - 29969788 q^{73} + 1284208 q^{74} - 51889380 q^{75} + 5112320 q^{76} - 909480 q^{77} + 265344 q^{78} + 35195816 q^{79} + 1720320 q^{80} + 77421726 q^{81} + 173472 q^{82} + 3472284 q^{83} - 1560576 q^{84} - 9905301 q^{85} - 10091968 q^{86} - 98926884 q^{87} + 1118208 q^{88} - 17705385 q^{89} + 6864480 q^{90} + 113728720 q^{91} + 41554176 q^{92} - 60183444 q^{93} - 84827328 q^{94} - 208276800 q^{95} + 786432 q^{96} - 74564404 q^{97} + 29548560 q^{98} + 124970652 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(74))\)

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
74.8.a \(\chi_{74}(1, \cdot)\) 74.8.a.a 4 1
74.8.a.b 4
74.8.a.c 6
74.8.a.d 7
74.8.b \(\chi_{74}(73, \cdot)\) 74.8.b.a 24 1
74.8.c \(\chi_{74}(47, \cdot)\) 74.8.c.a 22 2
74.8.c.b 24
74.8.e \(\chi_{74}(11, \cdot)\) 74.8.e.a 48 2
74.8.f \(\chi_{74}(7, \cdot)\) 74.8.f.a 60 6
74.8.f.b 66
74.8.h \(\chi_{74}(3, \cdot)\) 74.8.h.a 132 6

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(74))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(74)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 1}\)