Properties

Label 74.6
Level 74
Weight 6
Dimension 285
Nonzero newspaces 6
Newform subspaces 12
Sturm bound 2052
Trace bound 1

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Defining parameters

Level: \( N \) = \( 74 = 2 \cdot 37 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 12 \)
Sturm bound: \(2052\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(74))\).

Total New Old
Modular forms 891 285 606
Cusp forms 819 285 534
Eisenstein series 72 0 72

Trace form

\( 285 q + O(q^{10}) \) \( 285 q + 25884 q^{26} + 34992 q^{27} - 5952 q^{28} - 36756 q^{29} - 75168 q^{30} - 79812 q^{31} + 20088 q^{33} + 55008 q^{34} + 121068 q^{35} + 58320 q^{36} + 105756 q^{37} + 36144 q^{38} + 46116 q^{39} - 2880 q^{40} - 83052 q^{41} - 106272 q^{42} - 149112 q^{43} - 253692 q^{45} - 121248 q^{46} - 7596 q^{47} + 27648 q^{48} + 293712 q^{49} + 103644 q^{50} + 259380 q^{59} - 85275 q^{61} - 532548 q^{63} - 336879 q^{65} - 52236 q^{67} + 245520 q^{69} + 302760 q^{71} + 383688 q^{73} + 853380 q^{75} + 179208 q^{77} - 71640 q^{79} - 704880 q^{81} - 288396 q^{83} - 709479 q^{85} - 558468 q^{87} + 229725 q^{89} + 1373568 q^{91} + 864576 q^{92} + 1246212 q^{93} + 156960 q^{94} - 644400 q^{95} - 1614096 q^{97} - 1727424 q^{98} - 2069100 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(74))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
74.6.a \(\chi_{74}(1, \cdot)\) 74.6.a.a 1 1
74.6.a.b 1
74.6.a.c 3
74.6.a.d 5
74.6.a.e 5
74.6.b \(\chi_{74}(73, \cdot)\) 74.6.b.a 14 1
74.6.c \(\chi_{74}(47, \cdot)\) 74.6.c.a 14 2
74.6.c.b 16
74.6.e \(\chi_{74}(11, \cdot)\) 74.6.e.a 28 2
74.6.f \(\chi_{74}(7, \cdot)\) 74.6.f.a 48 6
74.6.f.b 54
74.6.h \(\chi_{74}(3, \cdot)\) 74.6.h.a 96 6

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(74))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(74)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)