Properties

Label 880.2.a
Level $880$
Weight $2$
Character orbit 880.a
Rep. character $\chi_{880}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $15$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(880))\).

Total New Old
Modular forms 156 20 136
Cusp forms 133 20 113
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.

\(2\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(8\)
Minus space\(-\)\(12\)

Trace form

\( 20 q - 4 q^{3} - 8 q^{7} + 20 q^{9} + O(q^{10}) \) \( 20 q - 4 q^{3} - 8 q^{7} + 20 q^{9} + 4 q^{15} + 8 q^{21} + 12 q^{23} + 20 q^{25} + 8 q^{27} + 8 q^{29} - 24 q^{31} + 16 q^{39} - 32 q^{43} + 8 q^{45} + 20 q^{47} + 4 q^{49} + 48 q^{51} + 4 q^{55} - 16 q^{57} + 32 q^{59} - 16 q^{61} + 8 q^{63} - 20 q^{67} - 8 q^{69} - 16 q^{71} - 16 q^{73} - 4 q^{75} + 12 q^{81} + 16 q^{83} - 16 q^{85} + 24 q^{87} - 32 q^{91} - 48 q^{93} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(880))\) 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 11
880.2.a.a 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(-3\) \(1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}-q^{7}+6q^{9}+q^{11}-6q^{13}+\cdots\)
880.2.a.b 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(-2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}-q^{11}-2q^{15}+\cdots\)
880.2.a.c 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-5q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots\)
880.2.a.d 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots\)
880.2.a.e 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}-q^{11}-4q^{13}+\cdots\)
880.2.a.f 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}+q^{11}+8q^{19}+\cdots\)
880.2.a.g 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-3q^{9}+q^{11}+6q^{13}+\cdots\)
880.2.a.h 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+q^{11}+2q^{13}+6q^{17}+\cdots\)
880.2.a.i 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(1\) \(1\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots\)
880.2.a.j 880.a 1.a $1$ $7.027$ \(\Q\) None \(0\) \(2\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+4q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
880.2.a.k 880.a 1.a $2$ $7.027$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
880.2.a.l 880.a 1.a $2$ $7.027$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
880.2.a.m 880.a 1.a $2$ $7.027$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+2q^{7}+5q^{9}-q^{11}+\cdots\)
880.2.a.n 880.a 1.a $2$ $7.027$ \(\Q(\sqrt{33}) \) None \(0\) \(1\) \(2\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-\beta q^{7}+(5+\beta )q^{9}+q^{11}+\cdots\)
880.2.a.o 880.a 1.a $2$ $7.027$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+\beta q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(880)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 2}\)