Properties

Label 1058.2.a
Level $1058$
Weight $2$
Character orbit 1058.a
Rep. character $\chi_{1058}(1,\cdot)$
Character field $\Q$
Dimension $43$
Newform subspaces $14$
Sturm bound $276$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1058 = 2 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1058.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(276\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1058))\).

Total New Old
Modular forms 162 43 119
Cusp forms 115 43 72
Eisenstein series 47 0 47

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

\(2\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(12\)
\(-\)\(+\)\(-\)\(15\)
\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(16\)
Minus space\(-\)\(27\)

Trace form

\( 43q + q^{2} + 43q^{4} - 4q^{5} + 4q^{7} + q^{8} + 47q^{9} + O(q^{10}) \) \( 43q + q^{2} + 43q^{4} - 4q^{5} + 4q^{7} + q^{8} + 47q^{9} + 4q^{10} - 2q^{11} + 2q^{13} - 4q^{14} + 43q^{16} + 2q^{17} - 3q^{18} + 2q^{19} - 4q^{20} + 2q^{22} + 33q^{25} - 2q^{26} + 4q^{28} - 6q^{29} - 4q^{31} + q^{32} - 2q^{34} + 12q^{35} + 47q^{36} + 4q^{37} - 2q^{38} + 4q^{40} - 10q^{41} - 10q^{43} - 2q^{44} + 12q^{45} - 4q^{47} + 31q^{49} + 7q^{50} + 2q^{52} + 4q^{53} - 12q^{55} - 4q^{56} + 2q^{58} - 16q^{59} + 8q^{61} - 4q^{62} - 12q^{63} + 43q^{64} + 8q^{65} + 10q^{67} + 2q^{68} - 24q^{70} - 8q^{71} - 3q^{72} - 14q^{73} - 4q^{74} - 16q^{75} + 2q^{76} - 8q^{77} - 8q^{78} + 12q^{79} - 4q^{80} + 19q^{81} + 2q^{82} - 14q^{83} - 4q^{85} + 10q^{86} - 16q^{87} + 2q^{88} + 6q^{89} - 12q^{90} - 8q^{91} - 8q^{94} - 12q^{95} - 6q^{97} + 9q^{98} + 6q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 23
1058.2.a.a \(1\) \(8.448\) \(\Q\) None \(-1\) \(-2\) \(-3\) \(-2\) \(+\) \(-\) \(q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}-2q^{7}+\cdots\)
1058.2.a.b \(1\) \(8.448\) \(\Q\) None \(-1\) \(-2\) \(3\) \(2\) \(+\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+3q^{5}+2q^{6}+2q^{7}+\cdots\)
1058.2.a.c \(1\) \(8.448\) \(\Q\) None \(-1\) \(0\) \(-4\) \(4\) \(+\) \(-\) \(q-q^{2}+q^{4}-4q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots\)
1058.2.a.d \(1\) \(8.448\) \(\Q\) None \(-1\) \(3\) \(-2\) \(2\) \(+\) \(-\) \(q-q^{2}+3q^{3}+q^{4}-2q^{5}-3q^{6}+2q^{7}+\cdots\)
1058.2.a.e \(1\) \(8.448\) \(\Q\) None \(-1\) \(3\) \(2\) \(-2\) \(+\) \(-\) \(q-q^{2}+3q^{3}+q^{4}+2q^{5}-3q^{6}-2q^{7}+\cdots\)
1058.2.a.f \(2\) \(8.448\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(0\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2\beta q^{5}-q^{6}+2\beta q^{7}+\cdots\)
1058.2.a.g \(2\) \(8.448\) \(\Q(\sqrt{3}) \) None \(2\) \(-4\) \(0\) \(0\) \(-\) \(-\) \(q+q^{2}-2q^{3}+q^{4}-\beta q^{5}-2q^{6}+2\beta q^{7}+\cdots\)
1058.2.a.h \(2\) \(8.448\) \(\Q(\sqrt{2}) \) None \(2\) \(4\) \(0\) \(0\) \(-\) \(+\) \(q+q^{2}+2q^{3}+q^{4}+2q^{6}+2\beta q^{7}+\cdots\)
1058.2.a.i \(4\) \(8.448\) \(\Q(\zeta_{24})^+\) None \(-4\) \(-4\) \(0\) \(0\) \(+\) \(+\) \(q-q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1058.2.a.j \(5\) \(8.448\) \(\Q(\zeta_{22})^+\) None \(-5\) \(0\) \(-2\) \(-9\) \(+\) \(+\) \(q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
1058.2.a.k \(5\) \(8.448\) \(\Q(\zeta_{22})^+\) None \(-5\) \(0\) \(2\) \(9\) \(+\) \(-\) \(q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
1058.2.a.l \(5\) \(8.448\) \(\Q(\zeta_{22})^+\) None \(5\) \(-2\) \(-8\) \(-7\) \(-\) \(-\) \(q+q^{2}+(-\beta _{1}-\beta _{3})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
1058.2.a.m \(5\) \(8.448\) \(\Q(\zeta_{22})^+\) None \(5\) \(-2\) \(8\) \(7\) \(-\) \(+\) \(q+q^{2}+(-\beta _{1}-\beta _{3})q^{3}+q^{4}+(2+\beta _{2}+\cdots)q^{5}+\cdots\)
1058.2.a.n \(8\) \(8.448\) 8.8.\(\cdots\).1 None \(8\) \(4\) \(0\) \(0\) \(-\) \(+\) \(q+q^{2}+\beta _{5}q^{3}+q^{4}+(\beta _{2}+\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1058))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1058)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 2}\)