Properties

Label 2010.2.i
Level 2010
Weight 2
Character orbit i
Rep. character \(\chi_{2010}(841,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 88
Newforms 9
Sturm bound 816
Trace bound 5

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2010.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 9 \)
Sturm bound: \(816\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2010, [\chi])\).

Total New Old
Modular forms 832 88 744
Cusp forms 800 88 712
Eisenstein series 32 0 32

Trace form

\(88q \) \(\mathstrut -\mathstrut 44q^{4} \) \(\mathstrut +\mathstrut 88q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(88q \) \(\mathstrut -\mathstrut 44q^{4} \) \(\mathstrut +\mathstrut 88q^{9} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut -\mathstrut 16q^{14} \) \(\mathstrut -\mathstrut 44q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 32q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 88q^{25} \) \(\mathstrut -\mathstrut 16q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 44q^{36} \) \(\mathstrut -\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut +\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 16q^{53} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 32q^{58} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 32q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut +\mathstrut 88q^{64} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 24q^{66} \) \(\mathstrut +\mathstrut 40q^{67} \) \(\mathstrut -\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 16q^{69} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 8q^{73} \) \(\mathstrut -\mathstrut 8q^{74} \) \(\mathstrut +\mathstrut 16q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 88q^{81} \) \(\mathstrut -\mathstrut 32q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 16q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 24q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 16q^{97} \) \(\mathstrut -\mathstrut 32q^{98} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2010, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2010.2.i.a \(2\) \(16.050\) \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(2\) \(-4\) \(q+(-1+\zeta_{6})q^{2}+q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots\)
2010.2.i.b \(10\) \(16.050\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-5\) \(-10\) \(10\) \(5\) \(q-\beta _{6}q^{2}-q^{3}+(-1+\beta _{6})q^{4}+q^{5}+\cdots\)
2010.2.i.c \(10\) \(16.050\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-5\) \(10\) \(-10\) \(3\) \(q-\beta _{5}q^{2}+q^{3}+(-1+\beta _{5})q^{4}-q^{5}+\cdots\)
2010.2.i.d \(10\) \(16.050\) 10.0.\(\cdots\).1 None \(-5\) \(10\) \(10\) \(1\) \(q-\beta _{5}q^{2}+q^{3}+(-1+\beta _{5})q^{4}+q^{5}+\cdots\)
2010.2.i.e \(10\) \(16.050\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(5\) \(-10\) \(-10\) \(-7\) \(q-\beta _{4}q^{2}-q^{3}+(-1-\beta _{4})q^{4}-q^{5}+\cdots\)
2010.2.i.f \(10\) \(16.050\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(5\) \(10\) \(10\) \(-1\) \(q+\beta _{5}q^{2}+q^{3}+(-1+\beta _{5})q^{4}+q^{5}+\cdots\)
2010.2.i.g \(12\) \(16.050\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(-12\) \(-12\) \(-1\) \(q-\beta _{6}q^{2}-q^{3}+(-1+\beta _{6})q^{4}-q^{5}+\cdots\)
2010.2.i.h \(12\) \(16.050\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(-12\) \(12\) \(3\) \(q+(1+\beta _{4})q^{2}-q^{3}+\beta _{4}q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
2010.2.i.i \(12\) \(16.050\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(12\) \(-12\) \(1\) \(q+\beta _{6}q^{2}+q^{3}+(-1+\beta _{6})q^{4}-q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2010, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2010, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(134, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 2}\)