Properties

Label 74.3
Level 74
Weight 3
Dimension 114
Nonzero newspaces 3
Newform subspaces 8
Sturm bound 1026
Trace bound 1

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Defining parameters

Level: \( N \) = \( 74 = 2 \cdot 37 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 8 \)
Sturm bound: \(1026\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(74))\).

Total New Old
Modular forms 378 114 264
Cusp forms 306 114 192
Eisenstein series 72 0 72

Trace form

\( 114 q + O(q^{10}) \) \( 114 q - 90 q^{26} - 432 q^{27} - 96 q^{28} - 252 q^{29} - 432 q^{30} - 540 q^{31} - 216 q^{33} - 144 q^{34} - 108 q^{35} + 84 q^{37} + 72 q^{38} + 252 q^{39} + 180 q^{40} + 540 q^{41} + 432 q^{42} + 504 q^{43} + 972 q^{45} + 720 q^{46} + 396 q^{47} + 144 q^{48} + 624 q^{49} + 126 q^{50} - 504 q^{59} - 540 q^{61} - 1080 q^{63} - 648 q^{65} - 216 q^{67} - 576 q^{69} - 144 q^{71} + 360 q^{75} + 288 q^{77} + 432 q^{79} + 1152 q^{81} + 360 q^{83} + 972 q^{85} + 1512 q^{87} + 720 q^{89} + 420 q^{91} - 648 q^{92} - 1836 q^{93} - 1152 q^{94} - 2160 q^{95} - 1872 q^{97} - 1728 q^{98} - 1980 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(74))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
74.3.d \(\chi_{74}(31, \cdot)\) 74.3.d.a 2 2
74.3.d.b 2
74.3.d.c 2
74.3.d.d 4
74.3.g \(\chi_{74}(23, \cdot)\) 74.3.g.a 8 4
74.3.g.b 12
74.3.i \(\chi_{74}(5, \cdot)\) 74.3.i.a 36 12
74.3.i.b 48

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(74))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(74)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)