Properties

Label 889.2.a
Level $889$
Weight $2$
Character orbit 889.a
Rep. character $\chi_{889}(1,\cdot)$
Character field $\Q$
Dimension $63$
Newform subspaces $4$
Sturm bound $170$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 889 = 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 889.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(170\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(889))\).

Total New Old
Modular forms 86 63 23
Cusp forms 83 63 20
Eisenstein series 3 0 3

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

\(7\)\(127\)FrickeDim.
\(+\)\(+\)\(+\)\(16\)
\(+\)\(-\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(20\)
\(-\)\(-\)\(+\)\(12\)
Plus space\(+\)\(28\)
Minus space\(-\)\(35\)

Trace form

\( 63q - q^{2} - 4q^{3} + 59q^{4} - 6q^{5} + q^{7} + 3q^{8} + 51q^{9} + O(q^{10}) \) \( 63q - q^{2} - 4q^{3} + 59q^{4} - 6q^{5} + q^{7} + 3q^{8} + 51q^{9} - 2q^{10} - 4q^{11} - 2q^{13} + 3q^{14} - 8q^{15} + 63q^{16} - 10q^{17} - 9q^{18} - 8q^{19} - 42q^{20} - 4q^{21} - 8q^{22} + 12q^{23} - 4q^{24} + 45q^{25} + 2q^{26} - 16q^{27} + 7q^{28} - 2q^{29} + 28q^{30} - 20q^{31} + 5q^{32} - 8q^{33} - 44q^{34} - 2q^{35} + 47q^{36} - 18q^{37} + 2q^{38} + 8q^{39} - 14q^{40} - 22q^{41} + 8q^{42} + 20q^{43} + 26q^{44} - 38q^{45} - 8q^{46} - 12q^{47} - 24q^{48} + 63q^{49} - 7q^{50} - 32q^{51} + 44q^{52} - 26q^{53} - 4q^{54} + 32q^{55} + 15q^{56} - 8q^{57} + 38q^{58} + 16q^{59} - 32q^{60} - 14q^{61} + 34q^{62} + 5q^{63} + 47q^{64} + 44q^{66} + 28q^{67} - 66q^{68} - 16q^{69} - 18q^{70} - 20q^{71} + 27q^{72} - 46q^{73} - 20q^{74} - 76q^{75} - 60q^{76} + 12q^{77} - 48q^{78} - 16q^{79} - 26q^{80} + 31q^{81} + 14q^{82} - 44q^{83} - 56q^{85} - 4q^{86} + 20q^{87} - 6q^{88} - 6q^{89} + 38q^{90} - 6q^{91} + 84q^{92} + 4q^{93} + 40q^{94} + 44q^{95} - 20q^{96} - 34q^{97} - q^{98} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(889))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 127
889.2.a.a \(12\) \(7.099\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-7\) \(-4\) \(-7\) \(12\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}-\beta _{10}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
889.2.a.b \(15\) \(7.099\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(4\) \(7\) \(-15\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots\)
889.2.a.c \(16\) \(7.099\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(-4\) \(-9\) \(-16\) \(+\) \(+\) \(q-\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
889.2.a.d \(20\) \(7.099\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(8\) \(0\) \(3\) \(20\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{16}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(889))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(889)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(127))\)\(^{\oplus 2}\)