Properties

Label 445.2.a
Level 445
Weight 2
Character orbit a
Rep. character \(\chi_{445}(1,\cdot)\)
Character field \(\Q\)
Dimension 29
Newforms 7
Sturm bound 90
Trace bound 3

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Defining parameters

Level: \( N \) = \( 445 = 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 445.a (trivial)
Character field: \(\Q\)
Newforms: \( 7 \)
Sturm bound: \(90\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(445))\).

Total New Old
Modular forms 46 29 17
Cusp forms 43 29 14
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.

\(5\)\(89\)FrickeDim.
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(13\)
Minus space\(-\)\(16\)

Trace form

\(29q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 23q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 33q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(29q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 23q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 33q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 7q^{18} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut +\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 29q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 32q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 29q^{32} \) \(\mathstrut +\mathstrut 28q^{33} \) \(\mathstrut -\mathstrut 10q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 21q^{36} \) \(\mathstrut -\mathstrut 26q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut -\mathstrut 9q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 8q^{44} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 20q^{48} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut +\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 42q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut +\mathstrut 10q^{58} \) \(\mathstrut -\mathstrut 28q^{60} \) \(\mathstrut -\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut -\mathstrut 33q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 36q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 75q^{72} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 14q^{74} \) \(\mathstrut +\mathstrut 24q^{76} \) \(\mathstrut +\mathstrut 20q^{77} \) \(\mathstrut +\mathstrut 52q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 45q^{81} \) \(\mathstrut -\mathstrut 2q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 20q^{84} \) \(\mathstrut -\mathstrut 14q^{85} \) \(\mathstrut +\mathstrut 16q^{86} \) \(\mathstrut -\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut +\mathstrut 7q^{90} \) \(\mathstrut +\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 12q^{92} \) \(\mathstrut -\mathstrut 20q^{93} \) \(\mathstrut -\mathstrut 12q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 20q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(445))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 89
445.2.a.a \(2\) \(3.553\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(2\) \(+\) \(+\) \(q-q^{2}+(-1-\beta )q^{3}-q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
445.2.a.b \(2\) \(3.553\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) \(-\) \(+\) \(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(3+\beta )q^{6}+\cdots\)
445.2.a.c \(2\) \(3.553\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(+\) \(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
445.2.a.d \(4\) \(3.553\) 4.4.725.1 None \(1\) \(-2\) \(-4\) \(2\) \(+\) \(+\) \(q+(1-\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}+\cdots\)
445.2.a.e \(4\) \(3.553\) 4.4.8069.1 None \(1\) \(4\) \(4\) \(12\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
445.2.a.f \(7\) \(3.553\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-4\) \(-8\) \(7\) \(-16\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{5})q^{3}+(2+\cdots)q^{4}+\cdots\)
445.2.a.g \(8\) \(3.553\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(6\) \(-8\) \(-6\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(445)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 2}\)