Properties

Label 560.2.a
Level $560$
Weight $2$
Character orbit 560.a
Rep. character $\chi_{560}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $9$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(560))\).

Total New Old
Modular forms 108 12 96
Cusp forms 85 12 73
Eisenstein series 23 0 23

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.
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(9\)

Trace form

\( 12q + 2q^{7} + 20q^{9} + O(q^{10}) \) \( 12q + 2q^{7} + 20q^{9} + 4q^{11} + 4q^{15} + 8q^{17} + 8q^{19} + 16q^{23} + 12q^{25} + 24q^{27} - 8q^{29} + 8q^{31} - 6q^{35} - 8q^{37} + 12q^{39} - 8q^{41} - 8q^{43} - 24q^{47} + 12q^{49} - 4q^{51} - 8q^{53} - 16q^{61} + 10q^{63} + 8q^{67} - 16q^{69} - 32q^{71} + 24q^{73} - 8q^{77} + 4q^{79} + 28q^{81} - 24q^{83} - 16q^{85} + 24q^{87} + 24q^{89} - 48q^{93} + 16q^{95} + 40q^{97} + 40q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(560))\) 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
560.2.a.a \(1\) \(4.472\) \(\Q\) None \(0\) \(-3\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q-3q^{3}-q^{5}+q^{7}+6q^{9}+5q^{11}+\cdots\)
560.2.a.b \(1\) \(4.472\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}-2q^{9}+3q^{11}+5q^{13}+\cdots\)
560.2.a.c \(1\) \(4.472\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots\)
560.2.a.d \(1\) \(4.472\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q-q^{5}+q^{7}-3q^{9}-4q^{11}-6q^{13}+\cdots\)
560.2.a.e \(1\) \(4.472\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}-2q^{9}+5q^{11}+q^{13}+\cdots\)
560.2.a.f \(1\) \(4.472\) \(\Q\) None \(0\) \(3\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(q+3q^{3}+q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots\)
560.2.a.g \(2\) \(4.472\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(q-\beta q^{3}+q^{5}-q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
560.2.a.h \(2\) \(4.472\) \(\Q(\sqrt{33}) \) None \(0\) \(1\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{3}-q^{5}+q^{7}+(5+\beta )q^{9}+(-4+\cdots)q^{11}+\cdots\)
560.2.a.i \(2\) \(4.472\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(560))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(560)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 2}\)