Properties

Label 280.2.a
Level $280$
Weight $2$
Character orbit 280.a
Rep. character $\chi_{280}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(280))\).

Total New Old
Modular forms 56 6 50
Cusp forms 41 6 35
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.

\(2\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(4\)

Trace form

\( 6 q - 4 q^{3} + 18 q^{9} + O(q^{10}) \) \( 6 q - 4 q^{3} + 18 q^{9} - 4 q^{11} + 12 q^{17} - 12 q^{19} - 8 q^{23} + 6 q^{25} - 16 q^{27} - 16 q^{31} + 24 q^{33} + 6 q^{35} - 4 q^{37} + 4 q^{39} + 4 q^{41} - 8 q^{43} + 16 q^{47} + 6 q^{49} - 4 q^{51} - 20 q^{53} - 8 q^{55} - 8 q^{57} + 12 q^{59} - 16 q^{61} - 8 q^{65} - 16 q^{67} - 40 q^{69} + 24 q^{71} + 12 q^{73} - 4 q^{75} - 8 q^{77} - 4 q^{79} + 22 q^{81} + 12 q^{83} - 4 q^{85} - 16 q^{87} + 4 q^{89} - 8 q^{91} - 40 q^{93} - 4 q^{95} + 44 q^{97} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(280))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 7
280.2.a.a $1$ $2.236$ \(\Q\) None \(0\) \(-3\) \(1\) \(1\) $+$ $-$ $-$ \(q-3q^{3}+q^{5}+q^{7}+6q^{9}-5q^{11}+\cdots\)
280.2.a.b $1$ $2.236$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ \(q-q^{3}-q^{5}-q^{7}-2q^{9}-5q^{11}+q^{13}+\cdots\)
280.2.a.c $2$ $2.236$ \(\Q(\sqrt{33}) \) None \(0\) \(-1\) \(-2\) \(-2\) $-$ $+$ $+$ \(q-\beta q^{3}-q^{5}-q^{7}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
280.2.a.d $2$ $2.236$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(2\) $-$ $-$ $-$ \(q+\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(280))\) into lower level spaces

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