Properties

Label 74.4.h
Level $74$
Weight $4$
Character orbit 74.h
Rep. character $\chi_{74}(3,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $60$
Newform subspaces $1$
Sturm bound $38$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 74.h (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(38\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(74, [\chi])\).

Total New Old
Modular forms 180 60 120
Cusp forms 156 60 96
Eisenstein series 24 0 24

Trace form

\( 60 q - 12 q^{3} + 18 q^{5} + 150 q^{7} - 96 q^{9} + O(q^{10}) \) \( 60 q - 12 q^{3} + 18 q^{5} + 150 q^{7} - 96 q^{9} - 60 q^{10} + 66 q^{11} + 48 q^{12} + 204 q^{13} - 36 q^{14} - 198 q^{15} - 90 q^{17} + 18 q^{19} + 72 q^{20} - 18 q^{21} + 492 q^{25} - 192 q^{26} + 426 q^{27} + 192 q^{28} + 360 q^{29} + 144 q^{30} - 624 q^{33} - 24 q^{34} - 1494 q^{35} - 2592 q^{36} - 1482 q^{37} + 960 q^{38} - 2298 q^{39} - 672 q^{40} + 828 q^{41} - 96 q^{42} - 168 q^{44} + 3384 q^{45} + 1884 q^{46} + 444 q^{47} + 288 q^{48} - 126 q^{49} + 1512 q^{50} - 552 q^{52} + 834 q^{53} - 1080 q^{54} - 864 q^{55} + 3318 q^{57} - 1332 q^{58} - 2112 q^{59} + 2532 q^{61} + 2520 q^{62} + 2082 q^{63} + 1920 q^{64} - 540 q^{65} - 4002 q^{67} + 1596 q^{69} - 1512 q^{70} - 4302 q^{71} - 5460 q^{73} + 2328 q^{74} + 9144 q^{75} + 72 q^{76} - 4392 q^{77} + 732 q^{78} - 1854 q^{79} - 2856 q^{81} - 1320 q^{83} - 1008 q^{84} + 888 q^{85} + 1512 q^{86} + 3936 q^{87} + 2592 q^{88} + 3198 q^{89} - 8868 q^{90} - 2088 q^{91} + 2832 q^{92} + 15408 q^{93} + 5568 q^{94} + 2166 q^{95} - 540 q^{97} + 4056 q^{98} - 840 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(74, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.4.h.a $60$ $4.366$ None \(0\) \(-12\) \(18\) \(150\)

Decomposition of \(S_{4}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(74, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)