Properties

Label 804.2.ba
Level 804
Weight 2
Character orbit ba
Rep. character \(\chi_{804}(41,\cdot)\)
Character field \(\Q(\zeta_{66})\)
Dimension 460
Newform subspaces 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.ba (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 2 \)
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 460 2380
Cusp forms 2600 460 2140
Eisenstein series 240 0 240

Trace form

\( 460q - 6q^{7} + 10q^{9} + O(q^{10}) \) \( 460q - 6q^{7} + 10q^{9} + 9q^{13} - 2q^{15} - 18q^{19} + 28q^{21} - 58q^{25} + 47q^{31} + 11q^{33} - 12q^{37} - 54q^{39} + 22q^{43} + 22q^{45} - 23q^{49} - 6q^{51} + 126q^{55} - 42q^{57} - 29q^{61} + 6q^{63} - q^{67} + 33q^{69} + 176q^{73} + 165q^{75} + 62q^{79} + 6q^{81} - 6q^{85} + 75q^{87} - 40q^{91} - 78q^{93} + 45q^{97} + 88q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
804.2.ba.a \(20\) \(6.420\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(6\) \(q+(-2\zeta_{33}-\zeta_{33}^{12})q^{3}+(1-\zeta_{33}+\cdots)q^{7}+\cdots\)
804.2.ba.b \(440\) \(6.420\) None \(0\) \(0\) \(0\) \(-12\)

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

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