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Properties

Label 74.8.f
Level $74$
Weight $8$
Character orbit 74.f
Rep. character $\chi_{74}(7,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $126$
Newform subspaces $2$
Sturm bound $76$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 8 \)
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: \(76\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(74, [\chi])\).

Total New Old
Modular forms 414 126 288
Cusp forms 390 126 264
Eisenstein series 24 0 24

Trace form

\( 126 q - 78 q^{3} - 165 q^{5} - 1836 q^{7} + 1536 q^{8} + 6474 q^{9} + O(q^{10}) \) \( 126 q - 78 q^{3} - 165 q^{5} - 1836 q^{7} + 1536 q^{8} + 6474 q^{9} + 6000 q^{10} + 7986 q^{11} - 4992 q^{12} + 162 q^{13} + 13488 q^{14} - 20820 q^{15} - 31161 q^{17} + 100110 q^{19} - 10560 q^{20} + 223326 q^{21} - 281268 q^{23} + 580365 q^{25} + 423144 q^{26} - 183378 q^{27} - 183168 q^{28} - 45786 q^{29} + 471744 q^{30} + 2356632 q^{31} - 211578 q^{33} - 660840 q^{34} - 2404590 q^{35} + 4758912 q^{36} - 837798 q^{37} - 2253696 q^{38} + 2828730 q^{39} + 1108992 q^{40} + 3754767 q^{41} + 1879968 q^{42} + 3145584 q^{43} - 290688 q^{44} - 1217670 q^{45} - 2751216 q^{46} - 1014978 q^{47} + 9445032 q^{49} - 517392 q^{50} - 3165696 q^{52} + 1414668 q^{53} - 481824 q^{54} + 6336630 q^{55} + 1362612 q^{57} - 3855288 q^{58} + 12206724 q^{59} - 13094106 q^{61} + 106848 q^{62} - 4170054 q^{63} - 16515072 q^{64} - 1081131 q^{65} - 8160150 q^{67} + 2505984 q^{68} - 4236810 q^{69} + 5959968 q^{70} - 25073952 q^{71} - 24545946 q^{73} + 16320504 q^{74} + 19727244 q^{75} + 6407040 q^{76} + 3167172 q^{77} - 17599056 q^{78} - 15728478 q^{79} + 3489792 q^{80} - 7684584 q^{81} + 161472 q^{82} + 32153040 q^{83} + 7112448 q^{84} - 17537505 q^{85} + 22501344 q^{86} - 85975716 q^{87} - 559104 q^{88} - 40498248 q^{89} - 76965432 q^{90} + 3337950 q^{91} + 12584832 q^{92} - 48769896 q^{93} - 38896320 q^{94} + 56656764 q^{95} - 11198520 q^{97} + 49143840 q^{98} + 26364066 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(74, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.8.f.a 74.f 37.f $60$ $23.116$ None 74.8.f.a \(0\) \(-39\) \(-624\) \(-918\) $\mathrm{SU}(2)[C_{9}]$
74.8.f.b 74.f 37.f $66$ $23.116$ None 74.8.f.b \(0\) \(-39\) \(459\) \(-918\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{8}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(74, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)