Properties

Label 74.6.f
Level $74$
Weight $6$
Character orbit 74.f
Rep. character $\chi_{74}(7,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $102$
Newform subspaces $2$
Sturm bound $57$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(57\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(74, [\chi])\).

Total New Old
Modular forms 294 102 192
Cusp forms 270 102 168
Eisenstein series 24 0 24

Trace form

\( 102 q - 6 q^{3} - 33 q^{5} + 228 q^{7} + 192 q^{8} - 186 q^{9} + O(q^{10}) \) \( 102 q - 6 q^{3} - 33 q^{5} + 228 q^{7} + 192 q^{8} - 186 q^{9} - 600 q^{10} - 726 q^{11} - 96 q^{12} + 246 q^{13} - 1320 q^{14} - 1092 q^{15} - 1833 q^{17} + 1518 q^{19} - 528 q^{20} + 2466 q^{21} + 396 q^{23} - 5895 q^{25} - 5004 q^{26} - 2154 q^{27} - 10464 q^{28} - 6126 q^{29} - 25056 q^{30} - 72648 q^{31} - 64806 q^{33} + 22956 q^{34} + 62466 q^{35} + 163296 q^{36} + 33750 q^{37} + 64032 q^{38} - 10518 q^{39} + 14208 q^{40} + 4215 q^{41} - 26448 q^{42} - 99408 q^{43} - 480 q^{44} - 65490 q^{45} - 58296 q^{46} - 1266 q^{47} + 16032 q^{49} + 122328 q^{50} - 68352 q^{52} - 38004 q^{53} + 19296 q^{54} - 192186 q^{55} + 216588 q^{57} - 35916 q^{58} + 301428 q^{59} + 22038 q^{61} + 128736 q^{62} - 11262 q^{63} - 208896 q^{64} - 49611 q^{65} - 114654 q^{67} - 45888 q^{68} + 702930 q^{69} - 25872 q^{70} + 43008 q^{71} - 155994 q^{73} + 57180 q^{74} - 234036 q^{75} + 24288 q^{76} - 277716 q^{77} + 246792 q^{78} - 442638 q^{79} + 89088 q^{80} - 12120 q^{81} - 73056 q^{82} - 413712 q^{83} - 84672 q^{84} - 72633 q^{85} - 197040 q^{86} + 307932 q^{87} + 45312 q^{88} + 303396 q^{89} + 192468 q^{90} + 708318 q^{91} + 343008 q^{92} + 558744 q^{93} + 42528 q^{94} - 1306812 q^{95} - 510984 q^{97} - 809424 q^{98} - 744654 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(74, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.6.f.a 74.f 37.f $48$ $11.868$ None \(0\) \(-3\) \(-72\) \(114\) $\mathrm{SU}(2)[C_{9}]$
74.6.f.b 74.f 37.f $54$ $11.868$ None \(0\) \(-3\) \(39\) \(114\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{6}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(74, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)