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Properties

Label 280.4.a
Level $280$
Weight $4$
Character orbit 280.a
Rep. character $\chi_{280}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $9$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(280))\).

Total New Old
Modular forms 152 18 134
Cusp forms 136 18 118
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.

\(2\)\(5\)\(7\)FrickeDim
\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)$+$\(3\)
\(-\)\(-\)\(-\)$-$\(1\)
Plus space\(+\)\(10\)
Minus space\(-\)\(8\)

Trace form

\( 18 q - 4 q^{3} + 102 q^{9} + O(q^{10}) \) \( 18 q - 4 q^{3} + 102 q^{9} - 100 q^{11} + 228 q^{17} + 180 q^{19} + 152 q^{23} + 450 q^{25} - 400 q^{27} + 176 q^{31} + 456 q^{33} - 210 q^{35} + 148 q^{37} - 252 q^{39} + 140 q^{41} - 888 q^{43} - 1168 q^{47} + 882 q^{49} - 116 q^{51} + 548 q^{53} - 360 q^{55} + 3624 q^{57} + 652 q^{59} + 720 q^{61} + 520 q^{65} - 2368 q^{67} + 968 q^{69} - 1176 q^{71} - 2908 q^{73} - 100 q^{75} + 616 q^{77} + 1996 q^{79} + 2530 q^{81} - 1556 q^{83} + 340 q^{85} + 816 q^{87} + 44 q^{89} - 840 q^{91} + 392 q^{93} - 20 q^{95} - 60 q^{97} - 824 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(280))\) 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
280.4.a.a 280.a 1.a $1$ $16.521$ \(\Q\) None \(0\) \(-4\) \(5\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{3}+5q^{5}+7q^{7}-11q^{9}+20q^{11}+\cdots\)
280.4.a.b 280.a 1.a $1$ $16.521$ \(\Q\) None \(0\) \(-1\) \(5\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+5q^{5}+7q^{7}-26q^{9}-39q^{11}+\cdots\)
280.4.a.c 280.a 1.a $1$ $16.521$ \(\Q\) None \(0\) \(5\) \(-5\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+5q^{3}-5q^{5}-7q^{7}-2q^{9}-39q^{11}+\cdots\)
280.4.a.d 280.a 1.a $1$ $16.521$ \(\Q\) None \(0\) \(7\) \(5\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+7q^{3}+5q^{5}+7q^{7}+22q^{9}+9q^{11}+\cdots\)
280.4.a.e 280.a 1.a $2$ $16.521$ \(\Q(\sqrt{73}) \) None \(0\) \(-3\) \(-10\) \(-14\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-5q^{5}-7q^{7}+(-8+\cdots)q^{9}+\cdots\)
280.4.a.f 280.a 1.a $3$ $16.521$ 3.3.11045.1 None \(0\) \(-6\) \(-15\) \(21\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}-5q^{5}+7q^{7}+(8-7\beta _{1}+\cdots)q^{9}+\cdots\)
280.4.a.g 280.a 1.a $3$ $16.521$ 3.3.11853.1 None \(0\) \(-6\) \(15\) \(-21\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+5q^{5}-7q^{7}+(3-6\beta _{1}+\cdots)q^{9}+\cdots\)
280.4.a.h 280.a 1.a $3$ $16.521$ 3.3.6053.1 None \(0\) \(2\) \(-15\) \(21\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-5q^{5}+7q^{7}+(13-\beta _{1}+\cdots)q^{9}+\cdots\)
280.4.a.i 280.a 1.a $3$ $16.521$ 3.3.78693.1 None \(0\) \(2\) \(15\) \(-21\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+5q^{5}-7q^{7}+(20-2\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(280))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(280)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 2}\)