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

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

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

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