↑

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 $13$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(882))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
882.2.a.a \(1\) \(7.043\) \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\cdots\)
882.2.a.b \(1\) \(7.043\) \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots\)
882.2.a.c \(1\) \(7.043\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{11}+\cdots\)
882.2.a.d \(1\) \(7.043\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\cdots\)
882.2.a.e \(1\) \(7.043\) \(\Q\) None \(-1\) \(0\) \(3\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots\)
882.2.a.f \(1\) \(7.043\) \(\Q\) None \(1\) \(0\) \(-4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+4q^{11}+\cdots\)
882.2.a.g \(1\) \(7.043\) \(\Q\) None \(1\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.h \(1\) \(7.043\) \(\Q\) None \(1\) \(0\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.i \(1\) \(7.043\) \(\Q\) None \(1\) \(0\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}+6q^{17}+\cdots\)
882.2.a.j \(1\) \(7.043\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.k \(1\) \(7.043\) \(\Q\) None \(1\) \(0\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.l \(1\) \(7.043\) \(\Q\) None \(1\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+4q^{11}+\cdots\)
882.2.a.m \(2\) \(7.043\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-4q^{11}+\cdots\)
882.2.a.n \(2\) \(7.043\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots\)
882.2.a.o \(2\) \(7.043\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+4q^{11}+\cdots\)

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

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