Properties

Label 804.2.o
Level 804
Weight 2
Character orbit o
Rep. character \(\chi_{804}(365,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 46
Newforms 4
Sturm bound 272
Trace bound 3

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Defining parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 4 \)
Sturm bound: \(272\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 284 46 238
Cusp forms 260 46 214
Eisenstein series 24 0 24

Trace form

\( 46q + 6q^{7} - 10q^{9} + O(q^{10}) \) \( 46q + 6q^{7} - 10q^{9} - 9q^{13} + 2q^{15} - 4q^{19} - 6q^{21} + 58q^{25} - 3q^{31} + 12q^{37} - 12q^{39} + 23q^{49} + 6q^{51} + 28q^{55} + 42q^{57} - 15q^{61} - 6q^{63} + 45q^{67} - 33q^{69} + 11q^{73} + 15q^{79} - 50q^{81} + 6q^{85} - 9q^{87} + 40q^{91} + 12q^{93} - 45q^{97} - 33q^{99} + O(q^{100}) \)

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.o.a \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-6\) \(q+(-1+2\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{7}+\cdots\)
804.2.o.b \(4\) \(6.420\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(-4\) \(8\) \(6\) \(q+(-1-\beta _{3})q^{3}+2q^{5}+(2+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
804.2.o.c \(4\) \(6.420\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(4\) \(-8\) \(6\) \(q+(1+\beta _{3})q^{3}-2q^{5}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
804.2.o.d \(36\) \(6.420\) None \(0\) \(0\) \(0\) \(0\)

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

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