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Properties

Label 74.6.e
Level $74$
Weight $6$
Character orbit 74.e
Rep. character $\chi_{74}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $1$
Sturm bound $57$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 6 \)
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: \(57\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 100 28 72
Cusp forms 92 28 64
Eisenstein series 8 0 8

Trace form

\( 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9} + O(q^{10}) \) \( 28 q - 20 q^{3} + 224 q^{4} - 90 q^{5} - 156 q^{7} - 586 q^{9} - 736 q^{10} + 464 q^{11} + 320 q^{12} + 72 q^{13} + 3960 q^{15} - 3584 q^{16} + 1530 q^{17} - 1944 q^{19} - 1440 q^{20} - 192 q^{21} - 3028 q^{25} - 5280 q^{26} + 36400 q^{27} + 2496 q^{28} - 4368 q^{30} - 2996 q^{33} + 1360 q^{34} - 21636 q^{35} - 18752 q^{36} + 45178 q^{37} - 14304 q^{38} + 14592 q^{39} - 5888 q^{40} + 12894 q^{41} - 26832 q^{42} + 3712 q^{44} - 22080 q^{46} - 39512 q^{47} + 10240 q^{48} + 8262 q^{49} - 44640 q^{50} + 1152 q^{52} + 47912 q^{53} - 101520 q^{54} + 70236 q^{55} + 99984 q^{57} + 51968 q^{58} - 74568 q^{59} - 8274 q^{61} - 22768 q^{62} - 137048 q^{63} - 114688 q^{64} + 33104 q^{65} - 7904 q^{67} - 69096 q^{69} + 65056 q^{70} + 9788 q^{71} + 256784 q^{73} - 8480 q^{74} + 518544 q^{75} - 31104 q^{76} - 86340 q^{77} + 89776 q^{78} - 82740 q^{79} - 174814 q^{81} + 19892 q^{83} - 6144 q^{84} - 167972 q^{85} + 119536 q^{86} - 200424 q^{87} - 223482 q^{89} + 59504 q^{90} - 53016 q^{91} + 198912 q^{92} - 227844 q^{93} + 158736 q^{94} - 140012 q^{95} - 168864 q^{98} - 401224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.6.e.a 74.e 37.e $28$ $11.868$ None 74.6.e.a \(0\) \(-20\) \(-90\) \(-156\) $\mathrm{SU}(2)[C_{6}]$

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

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