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Properties

Label 74.4.c
Level $74$
Weight $4$
Character orbit 74.c
Rep. character $\chi_{74}(47,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $18$
Newform subspaces $2$
Sturm bound $38$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 74.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(38\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 62 18 44
Cusp forms 54 18 36
Eisenstein series 8 0 8

Trace form

\( 18 q - 2 q^{2} - 10 q^{3} - 36 q^{4} - 11 q^{5} + 2 q^{7} + 16 q^{8} - 31 q^{9} + O(q^{10}) \) \( 18 q - 2 q^{2} - 10 q^{3} - 36 q^{4} - 11 q^{5} + 2 q^{7} + 16 q^{8} - 31 q^{9} - 36 q^{10} - 16 q^{11} - 40 q^{12} + 12 q^{13} + 16 q^{14} + 70 q^{15} - 144 q^{16} + 81 q^{17} - 90 q^{18} - 38 q^{19} - 44 q^{20} - 42 q^{21} + 144 q^{22} - 576 q^{23} + 180 q^{25} - 536 q^{26} + 1556 q^{27} + 8 q^{28} + 618 q^{29} + 312 q^{30} - 896 q^{31} - 32 q^{32} + 404 q^{33} + 114 q^{34} - 622 q^{35} + 248 q^{36} + 581 q^{37} - 416 q^{38} + 290 q^{39} + 72 q^{40} + 437 q^{41} - 352 q^{42} + 40 q^{43} + 32 q^{44} - 1486 q^{45} + 472 q^{46} + 248 q^{47} + 320 q^{48} + 237 q^{49} + 168 q^{50} - 964 q^{51} + 48 q^{52} + 140 q^{53} - 240 q^{54} - 532 q^{55} - 32 q^{56} - 262 q^{57} + 26 q^{58} + 158 q^{59} - 560 q^{60} + 13 q^{61} + 672 q^{62} - 2632 q^{63} + 1152 q^{64} + 460 q^{65} + 624 q^{66} + 1018 q^{67} - 648 q^{68} + 244 q^{69} + 192 q^{70} - 402 q^{71} - 360 q^{72} + 76 q^{73} - 76 q^{74} - 6184 q^{75} - 152 q^{76} + 1628 q^{77} + 2136 q^{78} - 554 q^{79} + 352 q^{80} - 3137 q^{81} - 1012 q^{82} + 3446 q^{83} + 336 q^{84} - 54 q^{85} + 1024 q^{86} + 324 q^{87} - 1152 q^{88} - 1235 q^{89} + 2146 q^{90} + 170 q^{91} + 1152 q^{92} + 5844 q^{93} + 312 q^{94} - 2446 q^{95} + 666 q^{97} + 126 q^{98} + 6608 q^{99} + O(q^{100}) \)

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.c.a 74.c 37.c $8$ $4.366$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(-5\) \(-10\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{2})q^{2}+(-\beta _{1}-\beta _{2})q^{3}-4\beta _{2}q^{4}+\cdots\)
74.4.c.b 74.c 37.c $10$ $4.366$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-10\) \(-5\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{3}q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots\)

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

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