Properties

Label 1145.2.a
Level 1145
Weight 2
Character orbit a
Rep. character \(\chi_{1145}(1,\cdot)\)
Character field \(\Q\)
Dimension 77
Newforms 6
Sturm bound 230
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1145 = 5 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1145.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(230\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1145))\).

Total New Old
Modular forms 116 77 39
Cusp forms 113 77 36
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.

\(5\)\(229\)FrickeDim.
\(+\)\(+\)\(+\)\(16\)
\(+\)\(-\)\(-\)\(22\)
\(-\)\(+\)\(-\)\(22\)
\(-\)\(-\)\(+\)\(17\)
Plus space\(+\)\(33\)
Minus space\(-\)\(44\)

Trace form

\( 77q - 3q^{2} + 79q^{4} + q^{5} - 4q^{6} + 4q^{7} - 15q^{8} + 73q^{9} + O(q^{10}) \) \( 77q - 3q^{2} + 79q^{4} + q^{5} - 4q^{6} + 4q^{7} - 15q^{8} + 73q^{9} + q^{10} - 8q^{11} - 16q^{12} + 10q^{13} - 12q^{14} + 79q^{16} - 6q^{17} - 23q^{18} + 7q^{20} + 28q^{21} - 36q^{22} - 8q^{23} - 20q^{24} + 77q^{25} + 18q^{26} - 12q^{27} + 4q^{28} - 18q^{29} + 8q^{30} + 4q^{31} - 43q^{32} - 12q^{33} - 10q^{34} - 8q^{35} + 51q^{36} + 10q^{37} - 32q^{38} - 40q^{39} + 9q^{40} - 14q^{41} - 12q^{42} + 12q^{43} + 5q^{45} + 36q^{46} - 24q^{47} - 20q^{48} + 101q^{49} - 3q^{50} - 20q^{51} + 6q^{52} + 10q^{53} + 24q^{54} - 4q^{55} - 36q^{56} + 8q^{57} - 6q^{58} - 12q^{59} + 12q^{60} + 14q^{61} + 4q^{62} + 59q^{64} - 14q^{65} + 20q^{66} - 66q^{68} + 24q^{69} + 24q^{70} - 47q^{72} - 2q^{73} - 14q^{74} - 8q^{76} - 16q^{77} - 32q^{78} + 15q^{80} + 61q^{81} - 50q^{82} - 4q^{83} + 104q^{84} + 2q^{85} - 80q^{86} + 12q^{87} - 148q^{88} + 18q^{89} - 23q^{90} + 8q^{91} - 12q^{92} + 40q^{93} - 32q^{94} + 12q^{95} - 52q^{96} + 10q^{97} + 77q^{98} - 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1145))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 229
1145.2.a.a \(1\) \(9.143\) \(\Q\) None \(-1\) \(-2\) \(-1\) \(-4\) \(+\) \(+\) \(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)
1145.2.a.b \(2\) \(9.143\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(0\) \(+\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}-q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
1145.2.a.c \(15\) \(9.143\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(4\) \(0\) \(-15\) \(-10\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
1145.2.a.d \(17\) \(9.143\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-8\) \(-12\) \(17\) \(-26\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1+\beta _{12})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1145.2.a.e \(20\) \(9.143\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-7\) \(4\) \(-20\) \(20\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
1145.2.a.f \(22\) \(9.143\) None \(7\) \(12\) \(22\) \(24\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1145))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1145)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(229))\)\(^{\oplus 2}\)