Properties

Label 380.2.c
Level $380$
Weight $2$
Character orbit 380.c
Rep. character $\chi_{380}(229,\cdot)$
Character field $\Q$
Dimension $10$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
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 66 10 56
Cusp forms 54 10 44
Eisenstein series 12 0 12

Trace form

\( 10 q - q^{5} - 10 q^{9} + O(q^{10}) \) \( 10 q - q^{5} - 10 q^{9} + 6 q^{11} - 10 q^{15} - 2 q^{19} - 4 q^{21} + 15 q^{25} + 4 q^{29} - 8 q^{31} - 13 q^{35} + 32 q^{39} - 20 q^{41} - 7 q^{45} - 16 q^{49} + 28 q^{51} + 21 q^{55} - 4 q^{59} + 10 q^{61} - 12 q^{65} + 20 q^{71} - 46 q^{75} - 32 q^{79} + 34 q^{81} - 15 q^{85} + 16 q^{89} + 16 q^{91} + q^{95} - 70 q^{99} + O(q^{100}) \)

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.c.a 380.c 5.b $4$ $3.034$ \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
380.2.c.b 380.c 5.b $6$ $3.034$ 6.0.14077504.2 None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)

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

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