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Properties

Label 920.2.a
Level $920$
Weight $2$
Character orbit 920.a
Rep. character $\chi_{920}(1,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $10$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(920))\).

Total New Old
Modular forms 152 22 130
Cusp forms 137 22 115
Eisenstein series 15 0 15

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

\(2\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(5\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(+\)$+$\(1\)
\(-\)\(-\)\(-\)$-$\(5\)
Plus space\(+\)\(6\)
Minus space\(-\)\(16\)

Trace form

\( 22 q + 8 q^{7} + 34 q^{9} + O(q^{10}) \) \( 22 q + 8 q^{7} + 34 q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{17} - 4 q^{19} + 8 q^{21} + 22 q^{25} - 8 q^{29} + 32 q^{31} + 24 q^{33} + 12 q^{35} + 8 q^{37} + 32 q^{39} + 12 q^{41} + 20 q^{43} + 22 q^{49} + 16 q^{51} + 24 q^{53} + 32 q^{57} - 12 q^{59} + 32 q^{61} - 12 q^{67} - 16 q^{71} + 36 q^{73} - 16 q^{77} - 16 q^{79} + 38 q^{81} - 28 q^{83} - 4 q^{85} - 48 q^{87} - 12 q^{89} + 24 q^{91} - 32 q^{93} - 8 q^{95} + 28 q^{97} - 28 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(920))\) 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 23
920.2.a.a 920.a 1.a $1$ $7.346$ \(\Q\) None \(0\) \(-3\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}-2q^{7}+6q^{9}+q^{13}+\cdots\)
920.2.a.b 920.a 1.a $1$ $7.346$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}+2q^{11}-5q^{13}+\cdots\)
920.2.a.c 920.a 1.a $1$ $7.346$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots\)
920.2.a.d 920.a 1.a $1$ $7.346$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}-2q^{9}+q^{13}-q^{15}+\cdots\)
920.2.a.e 920.a 1.a $2$ $7.346$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
920.2.a.f 920.a 1.a $2$ $7.346$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+2\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
920.2.a.g 920.a 1.a $3$ $7.346$ 3.3.621.1 None \(0\) \(0\) \(-3\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
920.2.a.h 920.a 1.a $3$ $7.346$ 3.3.2597.1 None \(0\) \(1\) \(3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(1-\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
920.2.a.i 920.a 1.a $3$ $7.346$ 3.3.229.1 None \(0\) \(2\) \(3\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+q^{5}+(2-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
920.2.a.j 920.a 1.a $5$ $7.346$ 5.5.13955077.1 None \(0\) \(0\) \(-5\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(920)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 2}\)