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Properties

Label 74.4.e
Level $74$
Weight $4$
Character orbit 74.e
Rep. character $\chi_{74}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
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.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{6})\)
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 60 20 40
Cusp forms 52 20 32
Eisenstein series 8 0 8

Trace form

\( 20 q - 2 q^{3} + 40 q^{4} - 18 q^{5} - 2 q^{7} - 76 q^{9} + O(q^{10}) \) \( 20 q - 2 q^{3} + 40 q^{4} - 18 q^{5} - 2 q^{7} - 76 q^{9} - 16 q^{10} - 16 q^{11} + 8 q^{12} - 150 q^{13} + 198 q^{15} - 160 q^{16} + 90 q^{17} + 162 q^{19} - 72 q^{20} - 30 q^{21} + 532 q^{25} + 528 q^{26} - 644 q^{27} + 8 q^{28} + 312 q^{30} - 596 q^{33} - 488 q^{34} - 342 q^{35} - 608 q^{36} - 112 q^{37} + 144 q^{38} + 1146 q^{39} - 32 q^{40} - 498 q^{41} - 120 q^{42} - 32 q^{44} + 424 q^{47} + 64 q^{48} + 84 q^{49} + 1008 q^{50} - 600 q^{52} - 142 q^{53} + 1080 q^{54} - 540 q^{55} + 138 q^{57} + 224 q^{58} + 1590 q^{59} - 1542 q^{61} + 8 q^{62} + 1864 q^{63} - 1280 q^{64} - 694 q^{65} + 62 q^{67} + 708 q^{69} - 368 q^{70} - 178 q^{71} - 528 q^{73} - 560 q^{74} - 7224 q^{75} + 648 q^{76} + 3468 q^{77} - 1736 q^{78} - 3474 q^{79} + 2414 q^{81} + 938 q^{83} - 240 q^{84} - 1100 q^{85} - 2120 q^{86} + 9420 q^{87} + 510 q^{89} + 2504 q^{90} + 666 q^{91} + 1344 q^{92} + 1728 q^{93} + 264 q^{94} + 4126 q^{95} - 816 q^{98} + 2312 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.4.e.a 74.e 37.e $20$ $4.366$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-2\) \(-18\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{11}q^{2}+\beta _{14}q^{3}+4\beta _{6}q^{4}+(-1+\cdots)q^{5}+\cdots\)

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

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