Properties

Label 1005.2.i
Level 1005
Weight 2
Character orbit i
Rep. character \(\chi_{1005}(766,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 92
Newforms 6
Sturm bound 272
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1005 = 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1005.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 6 \)
Sturm bound: \(272\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1005, [\chi])\).

Total New Old
Modular forms 280 92 188
Cusp forms 264 92 172
Eisenstein series 16 0 16

Trace form

\(92q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 40q^{4} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 92q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(92q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 40q^{4} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 48q^{8} \) \(\mathstrut +\mathstrut 92q^{9} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 28q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 8q^{18} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 20q^{28} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 10q^{31} \) \(\mathstrut +\mathstrut 56q^{32} \) \(\mathstrut +\mathstrut 20q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 40q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 12q^{43} \) \(\mathstrut -\mathstrut 40q^{44} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut +\mathstrut 28q^{47} \) \(\mathstrut +\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 34q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 40q^{52} \) \(\mathstrut +\mathstrut 80q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 32q^{57} \) \(\mathstrut -\mathstrut 16q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 112q^{62} \) \(\mathstrut +\mathstrut 12q^{63} \) \(\mathstrut +\mathstrut 80q^{64} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 24q^{66} \) \(\mathstrut -\mathstrut 2q^{67} \) \(\mathstrut +\mathstrut 96q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 48q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 40q^{74} \) \(\mathstrut -\mathstrut 4q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 56q^{77} \) \(\mathstrut -\mathstrut 12q^{78} \) \(\mathstrut -\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 16q^{80} \) \(\mathstrut +\mathstrut 92q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 24q^{84} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 12q^{87} \) \(\mathstrut -\mathstrut 28q^{88} \) \(\mathstrut +\mathstrut 88q^{91} \) \(\mathstrut -\mathstrut 16q^{92} \) \(\mathstrut +\mathstrut 10q^{93} \) \(\mathstrut -\mathstrut 112q^{94} \) \(\mathstrut -\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 24q^{96} \) \(\mathstrut -\mathstrut 14q^{97} \) \(\mathstrut +\mathstrut 60q^{98} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1005, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1005.2.i.a \(2\) \(8.025\) \(\Q(\sqrt{-3}) \) None \(2\) \(-2\) \(-2\) \(0\) \(q+(2-2\zeta_{6})q^{2}-q^{3}-2\zeta_{6}q^{4}-q^{5}+\cdots\)
1005.2.i.b \(10\) \(8.025\) 10.0.\(\cdots\).1 None \(2\) \(-10\) \(-10\) \(-5\) \(q+\beta _{1}q^{2}-q^{3}+(2\beta _{1}+2\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
1005.2.i.c \(12\) \(8.025\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(-12\) \(-12\) \(10\) \(q+(\beta _{4}+\beta _{8})q^{2}-q^{3}+(-2+\beta _{2}+2\beta _{5}+\cdots)q^{4}+\cdots\)
1005.2.i.d \(22\) \(8.025\) None \(1\) \(22\) \(-22\) \(3\)
1005.2.i.e \(22\) \(8.025\) None \(3\) \(22\) \(22\) \(9\)
1005.2.i.f \(24\) \(8.025\) None \(1\) \(-24\) \(24\) \(-5\)

Decomposition of \(S_{2}^{\mathrm{old}}(1005, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1005, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 2}\)