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Properties

Label 280.6.a
Level $280$
Weight $6$
Character orbit 280.a
Rep. character $\chi_{280}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $10$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.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 \(M_{6}(\Gamma_0(280))\).

Total New Old
Modular forms 248 30 218
Cusp forms 232 30 202
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
\(+\)\(+\)\(+\)$+$\(4\)
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(4\)
\(-\)\(+\)\(+\)$-$\(5\)
\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)$+$\(3\)
\(-\)\(-\)\(-\)$-$\(5\)
Plus space\(+\)\(14\)
Minus space\(-\)\(16\)

Trace form

\( 30 q + 44 q^{3} + 2298 q^{9} + O(q^{10}) \) \( 30 q + 44 q^{3} + 2298 q^{9} - 916 q^{11} - 3012 q^{17} - 1788 q^{19} - 2152 q^{23} + 18750 q^{25} + 176 q^{27} + 3888 q^{31} + 22776 q^{33} + 7350 q^{35} - 5476 q^{37} + 10020 q^{39} - 17164 q^{41} + 24008 q^{43} + 20144 q^{47} + 72030 q^{49} - 76388 q^{51} - 7540 q^{53} + 27800 q^{55} + 7128 q^{57} - 105956 q^{59} - 16784 q^{61} - 33800 q^{65} + 68256 q^{67} + 78104 q^{69} - 43896 q^{71} + 278108 q^{73} + 27500 q^{75} - 47432 q^{77} - 238228 q^{79} + 164398 q^{81} - 179492 q^{83} - 28900 q^{85} + 8496 q^{87} + 685268 q^{89} + 54488 q^{91} + 185240 q^{93} + 37900 q^{95} - 423524 q^{97} - 225464 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(280))\) 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
280.6.a.a 280.a 1.a $1$ $44.907$ \(\Q\) None \(0\) \(-12\) \(25\) \(-49\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-12q^{3}+5^{2}q^{5}-7^{2}q^{7}-99q^{9}+\cdots\)
280.6.a.b 280.a 1.a $1$ $44.907$ \(\Q\) None \(0\) \(4\) \(25\) \(-49\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{3}+5^{2}q^{5}-7^{2}q^{7}-227q^{9}+\cdots\)
280.6.a.c 280.a 1.a $2$ $44.907$ \(\Q(\sqrt{109}) \) None \(0\) \(2\) \(50\) \(-98\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+5^{2}q^{5}-7^{2}q^{7}+(194+\cdots)q^{9}+\cdots\)
280.6.a.d 280.a 1.a $2$ $44.907$ \(\Q(\sqrt{37}) \) None \(0\) \(26\) \(50\) \(-98\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(13-\beta )q^{3}+5^{2}q^{5}-7^{2}q^{7}+(74+\cdots)q^{9}+\cdots\)
280.6.a.e 280.a 1.a $3$ $44.907$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(6\) \(-75\) \(147\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}-5^{2}q^{5}+7^{2}q^{7}+(70+\cdots)q^{9}+\cdots\)
280.6.a.f 280.a 1.a $3$ $44.907$ 3.3.996509.1 None \(0\) \(14\) \(-75\) \(147\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(5+\beta _{2})q^{3}-5^{2}q^{5}+7^{2}q^{7}+(4+3\beta _{1}+\cdots)q^{9}+\cdots\)
280.6.a.g 280.a 1.a $4$ $44.907$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-13\) \(100\) \(196\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{1})q^{3}+5^{2}q^{5}+7^{2}q^{7}+(-7^{2}+\cdots)q^{9}+\cdots\)
280.6.a.h 280.a 1.a $4$ $44.907$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(5\) \(-100\) \(-196\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}-5^{2}q^{5}-7^{2}q^{7}+(142+\cdots)q^{9}+\cdots\)
280.6.a.i 280.a 1.a $5$ $44.907$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-3\) \(-125\) \(-245\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-5^{2}q^{5}-7^{2}q^{7}+(74+\cdots)q^{9}+\cdots\)
280.6.a.j 280.a 1.a $5$ $44.907$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(15\) \(125\) \(245\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(3-\beta _{1})q^{3}+5^{2}q^{5}+7^{2}q^{7}+(226+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(280))\) into lower level spaces

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