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Properties

Label 74.5
Level 74
Weight 5
Dimension 228
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 1710
Trace bound 1

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Defining parameters

Level: \( N \) = \( 74 = 2 \cdot 37 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(1710\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(74))\).

Total New Old
Modular forms 720 228 492
Cusp forms 648 228 420
Eisenstein series 72 0 72

Trace form

\( 228 q + O(q^{10}) \) \( 228 q - 4320 q^{26} - 11664 q^{27} - 768 q^{28} + 2268 q^{29} + 10368 q^{30} + 19980 q^{31} + 12312 q^{33} + 9216 q^{34} + 7452 q^{35} - 6132 q^{37} - 5184 q^{38} - 17388 q^{39} - 11520 q^{40} - 30780 q^{41} - 20736 q^{42} - 18648 q^{43} - 8748 q^{45} + 5760 q^{46} + 10692 q^{47} + 6912 q^{48} + 44304 q^{49} + 12096 q^{50} - 39312 q^{59} - 11880 q^{61} + 28080 q^{63} + 42768 q^{65} + 21168 q^{67} + 70272 q^{69} + 19872 q^{71} - 52560 q^{75} - 39744 q^{77} - 52704 q^{79} - 112896 q^{81} - 23760 q^{83} - 25272 q^{85} + 33264 q^{87} + 56160 q^{89} + 51204 q^{91} - 90720 q^{92} - 189108 q^{93} - 78336 q^{94} - 75600 q^{95} + 46800 q^{97} + 89856 q^{98} + 152460 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(74))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
74.5.d \(\chi_{74}(31, \cdot)\) 74.5.d.a 14 2
74.5.d.b 14
74.5.g \(\chi_{74}(23, \cdot)\) 74.5.g.a 28 4
74.5.g.b 28
74.5.i \(\chi_{74}(5, \cdot)\) 74.5.i.a 72 12
74.5.i.b 72

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(74))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(74)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)