Properties

Label 370.2.v
Level $370$
Weight $2$
Character orbit 370.v
Rep. character $\chi_{370}(99,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $120$
Newform subspaces $2$
Sturm bound $114$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.v (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(114\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(370, [\chi])\).

Total New Old
Modular forms 360 120 240
Cusp forms 312 120 192
Eisenstein series 48 0 48

Trace form

\( 120 q + 3 q^{5} - 12 q^{9} + O(q^{10}) \) \( 120 q + 3 q^{5} - 12 q^{9} + 12 q^{11} + 18 q^{14} + 12 q^{15} + 6 q^{19} - 3 q^{20} + 24 q^{21} - 33 q^{25} - 54 q^{26} + 24 q^{30} + 42 q^{34} + 6 q^{35} - 144 q^{36} + 24 q^{39} + 18 q^{40} - 114 q^{41} - 6 q^{44} + 54 q^{45} - 42 q^{46} - 12 q^{49} + 42 q^{50} + 6 q^{55} - 24 q^{59} + 84 q^{61} - 60 q^{64} - 45 q^{65} + 72 q^{69} - 12 q^{70} + 36 q^{71} + 6 q^{74} - 156 q^{75} - 6 q^{76} - 48 q^{79} - 72 q^{81} + 24 q^{84} + 3 q^{85} - 36 q^{86} + 6 q^{89} - 3 q^{90} + 114 q^{91} + 6 q^{94} - 144 q^{95} - 90 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(370, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
370.2.v.a 370.v 185.v $60$ $2.954$ None 370.2.v.a \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{18}]$
370.2.v.b 370.v 185.v $60$ $2.954$ None 370.2.v.a \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(370, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(370, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)