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Properties

Label 882.2.a
Level $882$
Weight $2$
Character orbit 882.a
Rep. character $\chi_{882}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $15$
Sturm bound $336$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(336\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(882))\).

Total New Old
Modular forms 200 18 182
Cusp forms 137 18 119
Eisenstein series 63 0 63

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

\(2\)\(3\)\(7\)FrickeDim
\(+\)\(+\)\(+\)$+$\(3\)
\(+\)\(+\)\(-\)$-$\(1\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(+\)$+$\(1\)
\(-\)\(-\)\(-\)$-$\(4\)
Plus space\(+\)\(7\)
Minus space\(-\)\(11\)

Trace form

\( 18 q + 18 q^{4} - 2 q^{5} + O(q^{10}) \) \( 18 q + 18 q^{4} - 2 q^{5} + 2 q^{10} - 2 q^{13} + 18 q^{16} + 8 q^{17} + 2 q^{19} - 2 q^{20} + 8 q^{22} + 8 q^{23} + 26 q^{25} + 10 q^{26} - 8 q^{29} + 4 q^{31} + 4 q^{34} - 16 q^{37} - 6 q^{38} + 2 q^{40} - 32 q^{43} - 12 q^{47} + 28 q^{50} - 2 q^{52} + 36 q^{53} - 8 q^{55} + 20 q^{58} - 2 q^{59} - 14 q^{61} + 4 q^{62} + 18 q^{64} + 4 q^{65} - 32 q^{67} + 8 q^{68} + 8 q^{71} - 12 q^{73} + 4 q^{74} + 2 q^{76} - 56 q^{79} - 2 q^{80} + 12 q^{82} - 10 q^{83} + 12 q^{85} - 8 q^{86} + 8 q^{88} - 12 q^{89} + 8 q^{92} - 12 q^{94} + 8 q^{95} + 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(882))\) 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 7
882.2.a.a 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\cdots\)
882.2.a.b 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots\)
882.2.a.c 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{11}+\cdots\)
882.2.a.d 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\cdots\)
882.2.a.e 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots\)
882.2.a.f 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+4q^{11}+\cdots\)
882.2.a.g 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.h 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.i 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}+6q^{17}+\cdots\)
882.2.a.j 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.k 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.l 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+4q^{11}+\cdots\)
882.2.a.m 882.a 1.a $2$ $7.043$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-4q^{11}+\cdots\)
882.2.a.n 882.a 1.a $2$ $7.043$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots\)
882.2.a.o 882.a 1.a $2$ $7.043$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+4q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(882))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(882)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)