Properties

Label 380.2.k
Level $380$
Weight $2$
Character orbit 380.k
Rep. character $\chi_{380}(267,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $108$
Newform subspaces $4$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
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 128 108 20
Cusp forms 112 108 4
Eisenstein series 16 0 16

Trace form

\( 108 q + O(q^{10}) \) \( 108 q - 16 q^{10} - 16 q^{12} - 4 q^{13} + 16 q^{16} - 20 q^{17} - 16 q^{21} - 16 q^{22} - 20 q^{25} - 32 q^{28} - 24 q^{30} - 40 q^{32} + 16 q^{33} - 16 q^{36} + 20 q^{37} + 24 q^{40} + 20 q^{45} - 48 q^{46} - 20 q^{48} + 4 q^{50} + 20 q^{52} - 44 q^{53} - 8 q^{56} - 32 q^{58} - 20 q^{60} + 24 q^{62} + 20 q^{65} + 72 q^{66} + 8 q^{68} + 76 q^{70} + 100 q^{72} + 36 q^{73} + 24 q^{77} + 24 q^{78} - 96 q^{80} - 28 q^{81} - 24 q^{82} + 4 q^{85} + 32 q^{86} - 20 q^{88} - 16 q^{90} - 40 q^{92} + 48 q^{93} - 40 q^{96} - 60 q^{97} - 64 q^{98} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
380.2.k.a 380.k 20.e $2$ $3.034$ \(\Q(\sqrt{-1}) \) None 380.2.k.a \(-2\) \(-2\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots\)
380.2.k.b 380.k 20.e $2$ $3.034$ \(\Q(\sqrt{-1}) \) None 380.2.k.a \(2\) \(2\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
380.2.k.c 380.k 20.e $52$ $3.034$ None 380.2.k.c \(-2\) \(-2\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
380.2.k.d 380.k 20.e $52$ $3.034$ None 380.2.k.c \(2\) \(2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(380, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)