Properties

Label 380.2.n
Level $380$
Weight $2$
Character orbit 380.n
Rep. character $\chi_{380}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $2$
Sturm bound $120$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(380, [\chi])\).

Total New Old
Modular forms 128 80 48
Cusp forms 112 80 32
Eisenstein series 16 0 16

Trace form

\( 80 q + 2 q^{4} - 2 q^{6} - 44 q^{9} + O(q^{10}) \) \( 80 q + 2 q^{4} - 2 q^{6} - 44 q^{9} - 6 q^{10} + 24 q^{13} + 2 q^{16} - 8 q^{17} + 24 q^{21} + 12 q^{24} - 40 q^{25} + 36 q^{26} + 20 q^{28} + 16 q^{30} - 30 q^{32} - 12 q^{33} - 54 q^{34} - 20 q^{36} + 50 q^{38} + 72 q^{41} - 42 q^{42} + 20 q^{44} + 18 q^{48} - 120 q^{49} - 18 q^{52} - 24 q^{53} - 22 q^{54} + 40 q^{57} - 60 q^{58} + 6 q^{60} + 16 q^{61} - 80 q^{62} - 16 q^{64} + 20 q^{66} + 52 q^{68} + 36 q^{70} + 84 q^{72} - 36 q^{73} + 12 q^{74} - 32 q^{76} - 16 q^{77} + 120 q^{78} + 16 q^{80} - 32 q^{81} - 42 q^{82} - 16 q^{85} + 96 q^{86} - 36 q^{89} + 78 q^{90} + 56 q^{92} - 8 q^{93} - 152 q^{96} + 12 q^{97} - 78 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(380, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.n.a 380.n 76.f $40$ $3.034$ None \(-3\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{6}]$
380.2.n.b 380.n 76.f $40$ $3.034$ None \(3\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)