Properties

Label 37.8.b
Level $37$
Weight $8$
Character orbit 37.b
Rep. character $\chi_{37}(36,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $1$
Sturm bound $25$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 37.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(25\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(37, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 20 20 0
Eisenstein series 2 2 0

Trace form

\( 20 q + 78 q^{3} - 844 q^{4} - 1746 q^{7} + 12362 q^{9} + O(q^{10}) \) \( 20 q + 78 q^{3} - 844 q^{4} - 1746 q^{7} + 12362 q^{9} - 882 q^{10} + 3498 q^{11} - 30374 q^{12} + 36116 q^{16} + 113482 q^{21} - 108112 q^{25} + 49278 q^{26} - 304110 q^{27} - 41192 q^{28} + 429776 q^{30} + 305646 q^{33} - 960356 q^{34} + 484758 q^{36} + 108732 q^{37} + 1049916 q^{38} - 496346 q^{40} - 1577742 q^{41} + 685266 q^{44} - 2906298 q^{46} - 1512786 q^{47} + 1522958 q^{48} + 3269246 q^{49} + 2999358 q^{53} + 405946 q^{58} + 3728310 q^{62} - 11995292 q^{63} - 11109700 q^{64} + 4251792 q^{65} + 3562224 q^{67} + 21605644 q^{70} - 15259086 q^{71} + 11088018 q^{73} - 2036544 q^{74} + 14882062 q^{75} - 2419122 q^{77} - 12178734 q^{78} - 17764972 q^{81} - 12873822 q^{83} + 9944396 q^{84} - 2698920 q^{85} + 15345336 q^{86} - 13219100 q^{90} + 48981192 q^{95} + 43111380 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(37, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
37.8.b.a 37.b 37.b $20$ $11.558$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(78\) \(0\) \(-1746\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(4+\beta _{4})q^{3}+(-42+\beta _{2}+\cdots)q^{4}+\cdots\)