Properties

Label 805.2.a
Level 805
Weight 2
Character orbit a
Rep. character \(\chi_{805}(1,\cdot)\)
Character field \(\Q\)
Dimension 43
Newforms 13
Sturm bound 192
Trace bound 11

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Defining parameters

Level: \( N \) = \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 805.a (trivial)
Character field: \(\Q\)
Newforms: \( 13 \)
Sturm bound: \(192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(805))\).

Total New Old
Modular forms 100 43 57
Cusp forms 93 43 50
Eisenstein series 7 0 7

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

\(5\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(8\)
Plus space\(+\)\(18\)
Minus space\(-\)\(25\)

Trace form

\(43q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 37q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 59q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(43q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 37q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 59q^{9} \) \(\mathstrut -\mathstrut 3q^{10} \) \(\mathstrut +\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 13q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 20q^{24} \) \(\mathstrut +\mathstrut 43q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 20q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 29q^{32} \) \(\mathstrut +\mathstrut 48q^{33} \) \(\mathstrut +\mathstrut 10q^{34} \) \(\mathstrut +\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut -\mathstrut 22q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 28q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut -\mathstrut 32q^{48} \) \(\mathstrut +\mathstrut 43q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut -\mathstrut 20q^{51} \) \(\mathstrut -\mathstrut 22q^{52} \) \(\mathstrut -\mathstrut 46q^{53} \) \(\mathstrut -\mathstrut 20q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 46q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 13q^{63} \) \(\mathstrut -\mathstrut 47q^{64} \) \(\mathstrut -\mathstrut 10q^{65} \) \(\mathstrut -\mathstrut 96q^{66} \) \(\mathstrut -\mathstrut 28q^{67} \) \(\mathstrut -\mathstrut 70q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut q^{70} \) \(\mathstrut -\mathstrut 40q^{71} \) \(\mathstrut -\mathstrut 75q^{72} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 50q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 28q^{78} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut +\mathstrut q^{80} \) \(\mathstrut +\mathstrut 131q^{81} \) \(\mathstrut +\mathstrut 46q^{82} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 10q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 17q^{92} \) \(\mathstrut +\mathstrut 40q^{93} \) \(\mathstrut -\mathstrut 12q^{94} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{96} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut +\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(805))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 7 23
805.2.a.a \(1\) \(6.428\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
805.2.a.b \(1\) \(6.428\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
805.2.a.c \(1\) \(6.428\) \(\Q\) None \(2\) \(-1\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
805.2.a.d \(1\) \(6.428\) \(\Q\) None \(2\) \(3\) \(-1\) \(-1\) \(+\) \(+\) \(-\) \(q+2q^{2}+3q^{3}+2q^{4}-q^{5}+6q^{6}+\cdots\)
805.2.a.e \(2\) \(6.428\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}-q^{5}+\cdots\)
805.2.a.f \(3\) \(6.428\) \(\Q(\zeta_{14})^+\) None \(-2\) \(0\) \(-3\) \(-3\) \(+\) \(+\) \(+\) \(q+(-1-\beta _{2})q^{2}+(-1+2\beta _{1}-\beta _{2})q^{3}+\cdots\)
805.2.a.g \(4\) \(6.428\) 4.4.2777.1 None \(-2\) \(-5\) \(4\) \(4\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{3})q^{2}+(-1-\beta _{1})q^{3}+(1+\cdots)q^{4}+\cdots\)
805.2.a.h \(4\) \(6.428\) 4.4.22545.1 None \(-1\) \(0\) \(-4\) \(-4\) \(+\) \(+\) \(-\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots\)
805.2.a.i \(4\) \(6.428\) 4.4.7537.1 None \(1\) \(4\) \(-4\) \(4\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.a.j \(4\) \(6.428\) 4.4.2777.1 None \(3\) \(6\) \(4\) \(-4\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
805.2.a.k \(5\) \(6.428\) 5.5.122821.1 None \(-3\) \(-6\) \(5\) \(-5\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
805.2.a.l \(5\) \(6.428\) 5.5.255877.1 None \(-1\) \(-4\) \(-5\) \(5\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
805.2.a.m \(8\) \(6.428\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(7\) \(8\) \(8\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(805))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(805)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 2}\)