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Properties

Label 920.4.a
Level $920$
Weight $4$
Character orbit 920.a
Rep. character $\chi_{920}(1,\cdot)$
Character field $\Q$
Dimension $66$
Newform subspaces $8$
Sturm bound $576$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 920.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(576\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(920))\).

Total New Old
Modular forms 440 66 374
Cusp forms 424 66 358
Eisenstein series 16 0 16

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
\(+\)\(+\)\(+\)$+$\(9\)
\(+\)\(+\)\(-\)$-$\(8\)
\(+\)\(-\)\(+\)$-$\(8\)
\(+\)\(-\)\(-\)$+$\(9\)
\(-\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(-\)$+$\(10\)
\(-\)\(-\)\(+\)$+$\(10\)
\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(38\)
Minus space\(-\)\(28\)

Trace form

\( 66 q - 16 q^{3} + 72 q^{7} + 534 q^{9} + O(q^{10}) \) \( 66 q - 16 q^{3} + 72 q^{7} + 534 q^{9} - 100 q^{11} - 20 q^{13} + 236 q^{17} + 540 q^{19} + 120 q^{21} + 1650 q^{25} - 832 q^{27} - 280 q^{29} - 480 q^{31} + 456 q^{33} - 420 q^{35} + 504 q^{37} + 288 q^{39} - 60 q^{41} - 12 q^{43} + 2114 q^{49} - 80 q^{51} - 1176 q^{53} + 2016 q^{57} + 532 q^{59} + 480 q^{61} + 4480 q^{63} + 212 q^{67} + 3408 q^{71} - 1684 q^{73} - 400 q^{75} + 1328 q^{77} + 1040 q^{79} + 7186 q^{81} + 164 q^{83} + 340 q^{85} + 400 q^{87} + 3804 q^{89} + 5944 q^{91} + 3520 q^{93} - 40 q^{95} + 2196 q^{97} + 4100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(920))\) 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
920.4.a.a 920.a 1.a $6$ $54.282$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-4\) \(30\) \(-14\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+5q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
920.4.a.b 920.a 1.a $6$ $54.282$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(2\) \(-30\) \(28\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-5q^{5}+(5+\beta _{2}+\beta _{4})q^{7}+\cdots\)
920.4.a.c 920.a 1.a $8$ $54.282$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-12\) \(40\) \(-31\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+5q^{5}+(-3-\beta _{1}+\cdots)q^{7}+\cdots\)
920.4.a.d 920.a 1.a $8$ $54.282$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-6\) \(-40\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-5q^{5}+\beta _{5}q^{7}+(8+\cdots)q^{9}+\cdots\)
920.4.a.e 920.a 1.a $9$ $54.282$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(-45\) \(25\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-5q^{5}+(3-\beta _{3})q^{7}+(6+2\beta _{1}+\cdots)q^{9}+\cdots\)
920.4.a.f 920.a 1.a $9$ $54.282$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(3\) \(45\) \(25\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+5q^{5}+(3-\beta _{3})q^{7}+(7+\beta _{1}+\cdots)q^{9}+\cdots\)
920.4.a.g 920.a 1.a $10$ $54.282$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-1\) \(-50\) \(28\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-5q^{5}+(3+\beta _{1}+\beta _{6})q^{7}+\cdots\)
920.4.a.h 920.a 1.a $10$ $54.282$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(5\) \(50\) \(14\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+5q^{5}+(1+\beta _{1}-\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(920))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(920)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 2}\)