Properties

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

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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: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(2010, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2010.2.i.a 2010.i 67.c $2$ $16.050$ \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots\)
2010.2.i.b 2010.i 67.c $10$ $16.050$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-5\) \(-10\) \(10\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{2}-q^{3}+(-1+\beta _{6})q^{4}+q^{5}+\cdots\)
2010.2.i.c 2010.i 67.c $10$ $16.050$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-5\) \(10\) \(-10\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}+q^{3}+(-1+\beta _{5})q^{4}-q^{5}+\cdots\)
2010.2.i.d 2010.i 67.c $10$ $16.050$ 10.0.\(\cdots\).1 None \(-5\) \(10\) \(10\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}+q^{3}+(-1+\beta _{5})q^{4}+q^{5}+\cdots\)
2010.2.i.e 2010.i 67.c $10$ $16.050$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(5\) \(-10\) \(-10\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}-q^{3}+(-1-\beta _{4})q^{4}-q^{5}+\cdots\)
2010.2.i.f 2010.i 67.c $10$ $16.050$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(5\) \(10\) \(10\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{5}q^{2}+q^{3}+(-1+\beta _{5})q^{4}+q^{5}+\cdots\)
2010.2.i.g 2010.i 67.c $12$ $16.050$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(-12\) \(-12\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{2}-q^{3}+(-1+\beta _{6})q^{4}-q^{5}+\cdots\)
2010.2.i.h 2010.i 67.c $12$ $16.050$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(-12\) \(12\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{4})q^{2}-q^{3}+\beta _{4}q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
2010.2.i.i 2010.i 67.c $12$ $16.050$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(12\) \(-12\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{2}+q^{3}+(-1+\beta _{6})q^{4}-q^{5}+\cdots\)

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

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