Properties

Label 6010.2.a
Level $6010$
Weight $2$
Character orbit 6010.a
Rep. character $\chi_{6010}(1,\cdot)$
Character field $\Q$
Dimension $199$
Newform subspaces $10$
Sturm bound $1806$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6010.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(1806\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6010))\).

Total New Old
Modular forms 906 199 707
Cusp forms 899 199 700
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(601\)FrickeDim
\(+\)\(+\)\(+\)$+$\(29\)
\(+\)\(+\)\(-\)$-$\(21\)
\(+\)\(-\)\(+\)$-$\(27\)
\(+\)\(-\)\(-\)$+$\(23\)
\(-\)\(+\)\(+\)$-$\(28\)
\(-\)\(+\)\(-\)$+$\(22\)
\(-\)\(-\)\(+\)$+$\(16\)
\(-\)\(-\)\(-\)$-$\(33\)
Plus space\(+\)\(90\)
Minus space\(-\)\(109\)

Trace form

\( 199 q - q^{2} - 4 q^{3} + 199 q^{4} - q^{5} - 4 q^{6} - 8 q^{7} - q^{8} + 195 q^{9} + O(q^{10}) \) \( 199 q - q^{2} - 4 q^{3} + 199 q^{4} - q^{5} - 4 q^{6} - 8 q^{7} - q^{8} + 195 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 6 q^{13} - 8 q^{14} + 4 q^{15} + 199 q^{16} - 2 q^{17} + 3 q^{18} - 20 q^{19} - q^{20} + 16 q^{21} - 8 q^{22} + 16 q^{23} - 4 q^{24} + 199 q^{25} + 10 q^{26} + 8 q^{27} - 8 q^{28} + 2 q^{29} - 4 q^{30} - q^{32} + 40 q^{33} - 2 q^{34} - 4 q^{35} + 195 q^{36} - 6 q^{37} + 24 q^{39} - q^{40} + 14 q^{41} + 32 q^{42} + 4 q^{44} + 3 q^{45} - 8 q^{46} + 24 q^{47} - 4 q^{48} + 159 q^{49} - q^{50} + 16 q^{51} - 6 q^{52} - 10 q^{53} + 8 q^{54} - 12 q^{55} - 8 q^{56} - 24 q^{57} + 30 q^{58} - 28 q^{59} + 4 q^{60} - 22 q^{61} + 16 q^{62} - 24 q^{63} + 199 q^{64} - 6 q^{65} + 16 q^{66} - 36 q^{67} - 2 q^{68} - 4 q^{70} + 16 q^{71} + 3 q^{72} - 10 q^{73} + 18 q^{74} - 4 q^{75} - 20 q^{76} - 16 q^{77} + 16 q^{78} - 40 q^{79} - q^{80} + 143 q^{81} + 14 q^{82} + 16 q^{83} + 16 q^{84} + 10 q^{85} - 4 q^{86} + 16 q^{87} - 8 q^{88} + 22 q^{89} - 13 q^{90} - 16 q^{91} + 16 q^{92} - 24 q^{93} - 16 q^{94} + 20 q^{95} - 4 q^{96} - 2 q^{97} + 39 q^{98} + 44 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6010))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 601
6010.2.a.a 6010.a 1.a $1$ $47.990$ \(\Q\) None \(-1\) \(-3\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{8}+\cdots\)
6010.2.a.b 6010.a 1.a $1$ $47.990$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots\)
6010.2.a.c 6010.a 1.a $16$ $47.990$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(-8\) \(16\) \(-10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
6010.2.a.d 6010.a 1.a $21$ $47.990$ None \(-21\) \(-1\) \(21\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$
6010.2.a.e 6010.a 1.a $21$ $47.990$ None \(-21\) \(8\) \(-21\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$
6010.2.a.f 6010.a 1.a $22$ $47.990$ None \(22\) \(-6\) \(-22\) \(-12\) $-$ $+$ $-$ $\mathrm{SU}(2)$
6010.2.a.g 6010.a 1.a $27$ $47.990$ None \(-27\) \(6\) \(27\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$
6010.2.a.h 6010.a 1.a $28$ $47.990$ None \(28\) \(4\) \(-28\) \(10\) $-$ $+$ $+$ $\mathrm{SU}(2)$
6010.2.a.i 6010.a 1.a $29$ $47.990$ None \(-29\) \(-10\) \(-29\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$
6010.2.a.j 6010.a 1.a $33$ $47.990$ None \(33\) \(6\) \(33\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6010))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(601))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1202))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3005))\)\(^{\oplus 2}\)