Properties

Label 580.2.a
Level $580$
Weight $2$
Character orbit 580.a
Rep. character $\chi_{580}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $180$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 580.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(180\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(580))\).

Total New Old
Modular forms 96 8 88
Cusp forms 85 8 77
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.

\(2\)\(5\)\(29\)FrickeDim
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(2\)
Minus space\(-\)\(6\)

Trace form

\( 8 q + 4 q^{3} - 4 q^{7} + 8 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{3} - 4 q^{7} + 8 q^{9} + 4 q^{11} - 8 q^{13} + 8 q^{17} + 12 q^{19} + 16 q^{21} - 4 q^{23} + 8 q^{25} + 16 q^{27} + 4 q^{31} + 24 q^{33} + 4 q^{35} - 8 q^{37} - 16 q^{39} + 12 q^{43} - 8 q^{45} + 4 q^{47} - 8 q^{49} - 16 q^{51} + 8 q^{53} - 8 q^{55} - 8 q^{57} + 8 q^{59} - 32 q^{61} - 20 q^{63} - 12 q^{67} - 8 q^{71} + 12 q^{73} + 4 q^{75} + 36 q^{77} - 20 q^{79} + 40 q^{81} - 12 q^{83} + 4 q^{85} + 16 q^{89} - 8 q^{91} + 16 q^{93} - 36 q^{97} + 36 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(580))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 29
580.2.a.a 580.a 1.a $1$ $4.631$ \(\Q\) None 580.2.a.a \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}-2q^{11}-2q^{13}-2q^{19}+\cdots\)
580.2.a.b 580.a 1.a $1$ $4.631$ \(\Q\) None 580.2.a.b \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{9}-4q^{11}-6q^{13}+\cdots\)
580.2.a.c 580.a 1.a $3$ $4.631$ 3.3.564.1 None 580.2.a.c \(0\) \(2\) \(-3\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
580.2.a.d 580.a 1.a $3$ $4.631$ 3.3.148.1 None 580.2.a.d \(0\) \(2\) \(3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(580))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(580)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 2}\)