Properties

Label 804.2.i
Level 804
Weight 2
Character orbit i
Rep. character \(\chi_{804}(37,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 22
Newforms 5
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 5 \)
Sturm bound: \(272\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 284 22 262
Cusp forms 260 22 238
Eisenstein series 24 0 24

Trace form

\(22q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 22q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(22q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 22q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 14q^{25} \) \(\mathstrut -\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 3q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 5q^{39} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 14q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 11q^{61} \) \(\mathstrut +\mathstrut 2q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 35q^{67} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 13q^{73} \) \(\mathstrut +\mathstrut 18q^{75} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut q^{79} \) \(\mathstrut +\mathstrut 22q^{81} \) \(\mathstrut -\mathstrut 18q^{83} \) \(\mathstrut +\mathstrut 6q^{85} \) \(\mathstrut +\mathstrut 6q^{87} \) \(\mathstrut -\mathstrut 72q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 7q^{93} \) \(\mathstrut -\mathstrut 46q^{95} \) \(\mathstrut +\mathstrut 49q^{97} \) \(\mathstrut +\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.i.a \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-4\) \(3\) \(q-q^{3}-2q^{5}+3\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
804.2.i.b \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(4\) \(-5\) \(q-q^{3}+2q^{5}-5\zeta_{6}q^{7}+q^{9}-5\zeta_{6}q^{11}+\cdots\)
804.2.i.c \(2\) \(6.420\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(4\) \(3\) \(q+q^{3}+2q^{5}+3\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{11}+\cdots\)
804.2.i.d \(8\) \(6.420\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-8\) \(2\) \(1\) \(q-q^{3}+\beta _{6}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+q^{9}+\cdots\)
804.2.i.e \(8\) \(6.420\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(-6\) \(0\) \(q+q^{3}+(-1-\beta _{2}+\beta _{5}-\beta _{6})q^{5}-\beta _{3}q^{7}+\cdots\)

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

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