Properties

Label 802.2.a
Level 802
Weight 2
Character orbit a
Rep. character \(\chi_{802}(1,\cdot)\)
Character field \(\Q\)
Dimension 33
Newforms 6
Sturm bound 201
Trace bound 3

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Defining parameters

Level: \( N \) = \( 802 = 2 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 802.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(201\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(802))\).

Total New Old
Modular forms 102 33 69
Cusp forms 99 33 66
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.

\(2\)\(401\)FrickeDim.
\(+\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(14\)
Minus space\(-\)\(19\)

Trace form

\(33q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 33q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 41q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(33q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 33q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 41q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 40q^{35} \) \(\mathstrut +\mathstrut 41q^{36} \) \(\mathstrut -\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 32q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 16q^{42} \) \(\mathstrut -\mathstrut 28q^{43} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut +\mathstrut 10q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut +\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 4q^{52} \) \(\mathstrut -\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 8q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 22q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 68q^{63} \) \(\mathstrut +\mathstrut 33q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 10q^{68} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 18q^{73} \) \(\mathstrut -\mathstrut 14q^{75} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 97q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 20q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 40q^{91} \) \(\mathstrut +\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 28q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut -\mathstrut 6q^{97} \) \(\mathstrut +\mathstrut 17q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(802))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 401
802.2.a.a \(1\) \(6.404\) \(\Q\) None \(1\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}+q^{8}+\cdots\)
802.2.a.b \(1\) \(6.404\) \(\Q\) None \(1\) \(0\) \(4\) \(-2\) \(-\) \(+\) \(q+q^{2}+q^{4}+4q^{5}-2q^{7}+q^{8}-3q^{9}+\cdots\)
802.2.a.c \(5\) \(6.404\) 5.5.38569.1 None \(5\) \(-6\) \(-9\) \(-1\) \(-\) \(-\) \(q+q^{2}+(-1+\beta _{4})q^{3}+q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
802.2.a.d \(7\) \(6.404\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(6\) \(5\) \(1\) \(+\) \(-\) \(q-q^{2}+(1-\beta _{5})q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
802.2.a.e \(9\) \(6.404\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(-6\) \(-5\) \(-7\) \(+\) \(+\) \(q-q^{2}+(-1-\beta _{7})q^{3}+q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
802.2.a.f \(10\) \(6.404\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(10\) \(9\) \(1\) \(-\) \(+\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{8})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(802))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(802)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 2}\)