Properties

Label 804.2.g
Level 804
Weight 2
Character orbit g
Rep. character \(\chi_{804}(401,\cdot)\)
Character field \(\Q\)
Dimension 22
Newforms 3
Sturm bound 272
Trace bound 1

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Defining parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(272\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(804, [\chi])\).

Total New Old
Modular forms 142 22 120
Cusp forms 130 22 108
Eisenstein series 12 0 12

Trace form

\(22q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(22q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 10q^{25} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 20q^{81} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut +\mathstrut 18q^{93} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
804.2.g.a \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-2\zeta_{6}q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
804.2.g.b \(4\) \(6.420\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(2\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(2+\cdots)q^{9}+\cdots\)
804.2.g.c \(16\) \(6.420\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{12}q^{5}+\beta _{10}q^{7}+\beta _{2}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(804, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(804, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 2}\)