Properties

Label 804.2.a
Level 804
Weight 2
Character orbit a
Rep. character \(\chi_{804}(1,\cdot)\)
Character field \(\Q\)
Dimension 12
Newforms 6
Sturm bound 272
Trace bound 5

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Defining parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(272\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(804))\).

Total New Old
Modular forms 142 12 130
Cusp forms 131 12 119
Eisenstein series 11 0 11

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

\(2\)\(3\)\(67\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(3\)
Minus space\(-\)\(9\)

Trace form

\( 12q + 12q^{9} + O(q^{10}) \) \( 12q + 12q^{9} + 4q^{11} + 4q^{13} + 4q^{15} - 2q^{17} + 10q^{19} + 4q^{21} + 6q^{23} + 20q^{25} + 2q^{29} + 8q^{31} + 4q^{33} + 4q^{35} + 18q^{37} + 24q^{41} - 20q^{43} - 2q^{47} + 36q^{49} - 4q^{51} + 4q^{53} + 8q^{57} - 6q^{59} + 12q^{65} + 2q^{67} + 8q^{69} - 4q^{71} - 18q^{73} - 8q^{75} - 4q^{77} - 24q^{79} + 12q^{81} - 12q^{83} + 24q^{85} - 12q^{87} + 30q^{89} + 16q^{91} + 4q^{93} - 8q^{95} + 4q^{97} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(804))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 67
804.2.a.a \(1\) \(6.420\) \(\Q\) None \(0\) \(-1\) \(-3\) \(3\) \(-\) \(+\) \(-\) \(q-q^{3}-3q^{5}+3q^{7}+q^{9}-2q^{11}+\cdots\)
804.2.a.b \(1\) \(6.420\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{9}-2q^{11}-4q^{13}-3q^{17}+\cdots\)
804.2.a.c \(1\) \(6.420\) \(\Q\) None \(0\) \(-1\) \(4\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+4q^{5}+q^{9}+2q^{13}-4q^{15}+\cdots\)
804.2.a.d \(1\) \(6.420\) \(\Q\) None \(0\) \(1\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(q+q^{3}-q^{5}-3q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
804.2.a.e \(3\) \(6.420\) 3.3.1076.1 None \(0\) \(-3\) \(-3\) \(-5\) \(-\) \(+\) \(+\) \(q-q^{3}+(-1-\beta _{1})q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
804.2.a.f \(5\) \(6.420\) 5.5.24571284.1 None \(0\) \(5\) \(3\) \(5\) \(-\) \(-\) \(-\) \(q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(804))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(804)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(268))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(402))\)\(^{\oplus 2}\)