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Properties

Label 1820.2.a
Level $1820$
Weight $2$
Character orbit 1820.a
Rep. character $\chi_{1820}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $9$
Sturm bound $672$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1820 = 2^{2} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1820.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(672\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1820))\).

Total New Old
Modular forms 348 24 324
Cusp forms 325 24 301
Eisenstein series 23 0 23

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

\(2\)\(5\)\(7\)\(13\)FrickeDim
\(-\)\(+\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(+\)\(-\)$+$\(4\)
\(-\)\(+\)\(-\)\(+\)$+$\(2\)
\(-\)\(+\)\(-\)\(-\)$-$\(4\)
\(-\)\(-\)\(+\)\(+\)$+$\(4\)
\(-\)\(-\)\(+\)\(-\)$-$\(2\)
\(-\)\(-\)\(-\)\(+\)$-$\(4\)
\(-\)\(-\)\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(12\)
Minus space\(-\)\(12\)

Trace form

\( 24 q - 8 q^{3} + 16 q^{9} + O(q^{10}) \) \( 24 q - 8 q^{3} + 16 q^{9} - 8 q^{11} - 16 q^{19} + 8 q^{23} + 24 q^{25} - 32 q^{27} + 8 q^{29} + 16 q^{31} + 16 q^{37} - 16 q^{41} + 16 q^{47} + 24 q^{49} + 16 q^{51} + 8 q^{53} - 16 q^{57} - 16 q^{59} - 8 q^{61} + 16 q^{63} - 8 q^{65} - 32 q^{67} - 32 q^{73} - 8 q^{75} - 8 q^{79} + 24 q^{81} - 8 q^{85} + 48 q^{87} - 16 q^{89} - 8 q^{95} - 32 q^{97} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1820))\) 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 7 13
1820.2.a.a 1820.a 1.a $2$ $14.533$ \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(-2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-q^{5}+q^{7}+(1+3\beta )q^{9}+\cdots\)
1820.2.a.b 1820.a 1.a $2$ $14.533$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(2\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+q^{5}+q^{7}+(-1+3\beta )q^{9}+\cdots\)
1820.2.a.c 1820.a 1.a $2$ $14.533$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}-q^{7}+(-2+\beta )q^{9}-2\beta q^{11}+\cdots\)
1820.2.a.d 1820.a 1.a $2$ $14.533$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-2\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+q^{7}+\beta q^{9}-2q^{11}+\cdots\)
1820.2.a.e 1820.a 1.a $2$ $14.533$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(2\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-q^{7}+(-2+\beta )q^{9}+2\beta q^{11}+\cdots\)
1820.2.a.f 1820.a 1.a $2$ $14.533$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots\)
1820.2.a.g 1820.a 1.a $4$ $14.533$ 4.4.27004.1 None \(0\) \(-3\) \(4\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1820.2.a.h 1820.a 1.a $4$ $14.533$ 4.4.30972.1 None \(0\) \(-1\) \(-4\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}-q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1820.2.a.i 1820.a 1.a $4$ $14.533$ 4.4.50908.1 None \(0\) \(1\) \(4\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+q^{5}+q^{7}+(2-\beta _{1}+\beta _{3})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1820))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1820)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(910))\)\(^{\oplus 2}\)