Properties

Label 2010.2.e
Level $2010$
Weight $2$
Character orbit 2010.e
Rep. character $\chi_{2010}(1609,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $10$
Sturm bound $816$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2010.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(816\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 416 64 352
Cusp forms 400 64 336
Eisenstein series 16 0 16

Trace form

\( 64 q - 64 q^{4} + 8 q^{5} - 4 q^{6} - 64 q^{9} + O(q^{10}) \) \( 64 q - 64 q^{4} + 8 q^{5} - 4 q^{6} - 64 q^{9} + 4 q^{10} - 8 q^{11} - 8 q^{14} + 4 q^{15} + 64 q^{16} - 8 q^{20} - 8 q^{21} + 4 q^{24} - 4 q^{25} + 24 q^{26} + 16 q^{29} + 8 q^{30} - 8 q^{31} - 16 q^{34} - 16 q^{35} + 64 q^{36} - 4 q^{40} + 24 q^{41} + 8 q^{44} - 8 q^{45} - 8 q^{46} - 32 q^{49} - 16 q^{50} + 4 q^{54} - 40 q^{55} + 8 q^{56} + 40 q^{59} - 4 q^{60} - 64 q^{64} - 56 q^{65} + 8 q^{70} + 8 q^{74} - 16 q^{75} + 72 q^{79} + 8 q^{80} + 64 q^{81} + 8 q^{84} - 8 q^{85} - 24 q^{89} - 4 q^{90} - 48 q^{91} - 8 q^{94} - 16 q^{95} - 4 q^{96} + 8 q^{99} + O(q^{100}) \)

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.e.a 2010.e 5.b $2$ $16.050$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
2010.2.e.b 2010.e 5.b $2$ $16.050$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
2010.2.e.c 2010.e 5.b $2$ $16.050$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}-q^{6}+\cdots\)
2010.2.e.d 2010.e 5.b $2$ $16.050$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots\)
2010.2.e.e 2010.e 5.b $2$ $16.050$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}-q^{6}+\cdots\)
2010.2.e.f 2010.e 5.b $2$ $16.050$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}+q^{6}+\cdots\)
2010.2.e.g 2010.e 5.b $8$ $16.050$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{4}q^{3}-q^{4}+(\beta _{1}-\beta _{5})q^{5}+\cdots\)
2010.2.e.h 2010.e 5.b $10$ $16.050$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
2010.2.e.i 2010.e 5.b $16$ $16.050$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}-\beta _{10}q^{3}-q^{4}+\beta _{2}q^{5}+\cdots\)
2010.2.e.j 2010.e 5.b $18$ $16.050$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+\beta _{7}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2010, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 2}\)