Properties

Label 1560.2.a
Level $1560$
Weight $2$
Character orbit 1560.a
Rep. character $\chi_{1560}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $17$
Sturm bound $672$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(672\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1560))\).

Total New Old
Modular forms 352 24 328
Cusp forms 321 24 297
Eisenstein series 31 0 31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(8\)
Minus space\(-\)\(16\)

Trace form

\( 24 q + 24 q^{9} + O(q^{10}) \) \( 24 q + 24 q^{9} + 4 q^{13} + 8 q^{17} + 24 q^{25} + 8 q^{29} + 8 q^{33} + 24 q^{37} + 16 q^{41} + 48 q^{49} - 8 q^{53} + 8 q^{57} + 16 q^{59} - 8 q^{61} - 8 q^{67} + 16 q^{69} - 32 q^{71} + 48 q^{73} + 16 q^{77} + 24 q^{79} + 24 q^{81} - 32 q^{83} + 8 q^{85} + 8 q^{87} + 48 q^{89} + 24 q^{93} + 16 q^{95} + 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1560))\) 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 3 5 13
1560.2.a.a 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+q^{13}+q^{15}-6q^{17}+\cdots\)
1560.2.a.b 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+4q^{11}+q^{13}+q^{15}+\cdots\)
1560.2.a.c 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(-1\) \(1\) \(-5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-5q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
1560.2.a.d 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-4q^{11}+q^{13}-q^{15}+\cdots\)
1560.2.a.e 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
1560.2.a.f 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(-1\) \(1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
1560.2.a.g 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
1560.2.a.h 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
1560.2.a.i 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-q^{13}-q^{15}+2q^{17}+\cdots\)
1560.2.a.j 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(1\) \(1\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
1560.2.a.k 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}+q^{13}+q^{15}+\cdots\)
1560.2.a.l 1560.a 1.a $1$ $12.457$ \(\Q\) None \(0\) \(1\) \(1\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}+q^{13}+q^{15}+\cdots\)
1560.2.a.m 1560.a 1.a $2$ $12.457$ \(\Q(\sqrt{41}) \) None \(0\) \(-2\) \(-2\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
1560.2.a.n 1560.a 1.a $2$ $12.457$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-2\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
1560.2.a.o 1560.a 1.a $2$ $12.457$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(2\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
1560.2.a.p 1560.a 1.a $3$ $12.457$ 3.3.1849.1 None \(0\) \(3\) \(-3\) \(5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(2-\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
1560.2.a.q 1560.a 1.a $3$ $12.457$ 3.3.940.1 None \(0\) \(3\) \(3\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+(2+\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1560))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1560)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(780))\)\(^{\oplus 2}\)