Properties

Label 804.2.y
Level 804
Weight 2
Character orbit y
Rep. character \(\chi_{804}(49,\cdot)\)
Character field \(\Q(\zeta_{33})\)
Dimension 220
Newforms 2
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.y (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{33})\)
Newforms: \( 2 \)
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 2840 220 2620
Cusp forms 2600 220 2380
Eisenstein series 240 0 240

Trace form

\( 220q + 2q^{3} - 2q^{7} - 22q^{9} + O(q^{10}) \) \( 220q + 2q^{3} - 2q^{7} - 22q^{9} - 2q^{11} - q^{13} - 18q^{15} + 4q^{17} - 20q^{19} - 4q^{21} + 6q^{23} - 14q^{25} + 2q^{27} - 8q^{29} + 47q^{31} - 2q^{33} - 2q^{35} - 30q^{37} - 5q^{39} - 72q^{41} - 44q^{43} - 80q^{47} + 9q^{49} - 4q^{51} + 36q^{53} - 22q^{55} + 43q^{57} + 56q^{59} + 33q^{61} + 9q^{63} + 200q^{65} + 9q^{67} + 28q^{69} + 172q^{71} + 24q^{73} + 70q^{75} + 240q^{77} + 100q^{79} - 22q^{81} + 62q^{83} - 6q^{85} - 6q^{87} + 6q^{89} - 24q^{91} - 7q^{93} - 20q^{95} + 39q^{97} - 2q^{99} + O(q^{100}) \)

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.y.a \(100\) \(6.420\) None \(0\) \(-10\) \(2\) \(-3\)
804.2.y.b \(120\) \(6.420\) None \(0\) \(12\) \(-2\) \(1\)

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

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