Properties

Label 804.2.q
Level 804
Weight 2
Character orbit q
Rep. character \(\chi_{804}(25,\cdot)\)
Character field \(\Q(\zeta_{11})\)
Dimension 120
Newforms 2
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.q (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{11})\)
Newforms: \( 2 \)
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 1420 120 1300
Cusp forms 1300 120 1180
Eisenstein series 120 0 120

Trace form

\( 120q - 12q^{9} + O(q^{10}) \) \( 120q - 12q^{9} - 4q^{11} - 4q^{13} + 18q^{15} + 2q^{17} + 12q^{19} - 4q^{21} - 6q^{23} - 20q^{25} + 20q^{29} - 52q^{31} - 4q^{33} - 4q^{35} + 4q^{37} + 42q^{41} + 42q^{43} + 68q^{47} - 36q^{49} + 4q^{51} + 18q^{53} + 22q^{55} + 14q^{57} + 94q^{59} + 88q^{61} + 76q^{65} + 20q^{67} + 14q^{69} + 92q^{71} + 18q^{73} + 52q^{75} - 84q^{77} + 2q^{79} - 12q^{81} + 34q^{83} - 24q^{85} + 12q^{87} + 36q^{89} - 16q^{91} - 4q^{93} + 74q^{95} - 92q^{97} - 4q^{99} + O(q^{100}) \)

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.q.a \(60\) \(6.420\) None \(0\) \(-6\) \(-2\) \(-2\)
804.2.q.b \(60\) \(6.420\) None \(0\) \(6\) \(2\) \(2\)

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

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