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Properties

Label 74.4
Level 74
Weight 4
Dimension 171
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 1368
Trace bound 1

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Defining parameters

Level: \( N \) = \( 74 = 2 \cdot 37 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(1368\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(74))\).

Total New Old
Modular forms 549 171 378
Cusp forms 477 171 306
Eisenstein series 72 0 72

Trace form

\( 171 q + O(q^{10}) \) \( 171 q + 666 q^{26} + 2592 q^{27} + 432 q^{28} + 720 q^{29} + 432 q^{30} - 648 q^{31} - 1728 q^{33} - 2160 q^{34} - 3672 q^{35} - 1620 q^{36} - 3024 q^{37} - 1224 q^{38} - 2520 q^{39} - 1080 q^{40} - 1728 q^{41} - 432 q^{42} + 432 q^{43} + 3888 q^{45} + 3888 q^{46} + 2664 q^{47} + 1152 q^{48} + 5760 q^{49} + 1314 q^{50} + 4932 q^{59} + 3735 q^{61} + 3996 q^{63} - 81 q^{65} - 1116 q^{67} - 7632 q^{69} - 4824 q^{71} - 5256 q^{73} - 12780 q^{75} - 4392 q^{77} - 3096 q^{79} - 2448 q^{81} + 612 q^{83} + 4779 q^{85} + 11772 q^{87} + 7515 q^{89} + 11628 q^{91} + 8352 q^{92} + 21168 q^{93} + 11664 q^{94} + 18720 q^{95} + 10368 q^{97} + 6624 q^{98} + 3960 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(74))\)

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
74.4.a \(\chi_{74}(1, \cdot)\) 74.4.a.a 1 1
74.4.a.b 1
74.4.a.c 3
74.4.a.d 4
74.4.b \(\chi_{74}(73, \cdot)\) 74.4.b.a 10 1
74.4.c \(\chi_{74}(47, \cdot)\) 74.4.c.a 8 2
74.4.c.b 10
74.4.e \(\chi_{74}(11, \cdot)\) 74.4.e.a 20 2
74.4.f \(\chi_{74}(7, \cdot)\) 74.4.f.a 24 6
74.4.f.b 30
74.4.h \(\chi_{74}(3, \cdot)\) 74.4.h.a 60 6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(74))\) into lower level spaces

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