Properties

Label 380.2.a
Level $380$
Weight $2$
Character orbit 380.a
Rep. character $\chi_{380}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $120$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(380))\).

Total New Old
Modular forms 66 6 60
Cusp forms 55 6 49
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(19\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(3\)

Trace form

\( 6 q + 2 q^{5} + 6 q^{9} + O(q^{10}) \) \( 6 q + 2 q^{5} + 6 q^{9} - 8 q^{11} - 4 q^{13} - 4 q^{15} + 4 q^{17} + 8 q^{21} - 16 q^{23} + 6 q^{25} - 12 q^{27} - 4 q^{29} - 8 q^{31} - 4 q^{33} - 8 q^{37} + 24 q^{39} - 20 q^{41} + 8 q^{43} + 10 q^{45} + 8 q^{47} - 2 q^{49} - 8 q^{51} + 4 q^{57} - 4 q^{61} + 32 q^{63} - 8 q^{65} + 4 q^{67} + 8 q^{69} + 16 q^{71} - 12 q^{73} + 16 q^{77} - 16 q^{79} + 46 q^{81} + 8 q^{83} - 12 q^{85} + 24 q^{87} - 4 q^{89} + 24 q^{93} - 16 q^{97} - 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(380))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 19
380.2.a.a 380.a 1.a $1$ $3.034$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}-4q^{13}+\cdots\)
380.2.a.b 380.a 1.a $1$ $3.034$ \(\Q\) None \(0\) \(2\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+6q^{13}+\cdots\)
380.2.a.c 380.a 1.a $2$ $3.034$ \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}+q^{5}+(-2-2\beta )q^{7}+\cdots\)
380.2.a.d 380.a 1.a $2$ $3.034$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+2q^{7}+(1+2\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(380))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(380)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 2}\)