Properties

Label 380.2.l
Level $380$
Weight $2$
Character orbit 380.l
Rep. character $\chi_{380}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 132 20 112
Cusp forms 108 20 88
Eisenstein series 24 0 24

Trace form

\( 20 q + 2 q^{5} - 2 q^{7} + O(q^{10}) \) \( 20 q + 2 q^{5} - 2 q^{7} + 8 q^{11} + 10 q^{17} + 20 q^{23} + 14 q^{25} + 14 q^{35} - 26 q^{43} - 40 q^{45} - 6 q^{47} - 16 q^{55} + 24 q^{57} + 16 q^{61} + 2 q^{63} - 54 q^{73} + 10 q^{77} - 68 q^{81} + 20 q^{83} - 52 q^{85} - 80 q^{87} + 8 q^{93} + 22 q^{95} + O(q^{100}) \)

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.l.a 380.l 95.g $8$ $3.034$ 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) 380.2.l.a \(0\) \(0\) \(-2\) \(-6\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{6}q^{5}+(-1+\beta _{3}+\beta _{5}-\beta _{6}+\beta _{7})q^{7}+\cdots\)
380.2.l.b 380.l 95.g $12$ $3.034$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 380.2.l.b \(0\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(\beta _{3}-\beta _{8})q^{5}+\beta _{6}q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(380, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)