Properties

Label 6033.2.a
Level $6033$
Weight $2$
Character orbit 6033.a
Rep. character $\chi_{6033}(1,\cdot)$
Character field $\Q$
Dimension $335$
Newform subspaces $5$
Sturm bound $1341$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 6033 = 3 \cdot 2011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6033.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(1341\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6033))\).

Total New Old
Modular forms 672 335 337
Cusp forms 669 335 334
Eisenstein series 3 0 3

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

\(3\)\(2011\)FrickeDim
\(+\)\(+\)$+$\(84\)
\(+\)\(-\)$-$\(83\)
\(-\)\(+\)$-$\(97\)
\(-\)\(-\)$+$\(71\)
Plus space\(+\)\(155\)
Minus space\(-\)\(180\)

Trace form

\( 335 q + q^{2} + q^{3} + 339 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 335 q^{9} + O(q^{10}) \) \( 335 q + q^{2} + q^{3} + 339 q^{4} - 2 q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 335 q^{9} - 2 q^{10} + 8 q^{11} + 7 q^{12} - 6 q^{13} + 4 q^{14} - 2 q^{15} + 359 q^{16} - 10 q^{17} + q^{18} + 16 q^{19} + 10 q^{20} + 4 q^{21} + 12 q^{23} - 3 q^{24} + 321 q^{25} + 2 q^{26} + q^{27} - 16 q^{28} - 2 q^{29} - 10 q^{30} - 12 q^{31} - 15 q^{32} - 8 q^{33} - 30 q^{34} + 339 q^{36} + 14 q^{37} - 52 q^{38} + 6 q^{39} - 22 q^{40} + 6 q^{41} - 20 q^{42} + 16 q^{43} + 20 q^{44} - 2 q^{45} - 8 q^{47} - q^{48} + 339 q^{49} - 29 q^{50} + 10 q^{51} - 70 q^{52} - 18 q^{53} + q^{54} + 16 q^{55} + 16 q^{56} - 22 q^{58} - 8 q^{59} - 6 q^{60} + 6 q^{61} + 24 q^{62} + 4 q^{63} + 399 q^{64} - 8 q^{65} - 20 q^{66} - 16 q^{67} + 2 q^{68} + 12 q^{69} - 4 q^{70} + 12 q^{71} - 3 q^{72} - 10 q^{73} + 42 q^{74} + 15 q^{75} + 72 q^{76} + 28 q^{77} + 26 q^{78} + 20 q^{79} + 2 q^{80} + 335 q^{81} + 6 q^{82} + 32 q^{83} + 4 q^{84} - 12 q^{85} + 68 q^{86} - 22 q^{87} + 48 q^{88} + 2 q^{89} - 2 q^{90} + 48 q^{91} + 16 q^{92} - 8 q^{93} - 4 q^{94} - 8 q^{95} + 5 q^{96} - 14 q^{97} + 37 q^{98} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6033))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 2011
6033.2.a.a 6033.a 1.a $1$ $48.174$ \(\Q\) None \(0\) \(-1\) \(3\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+3q^{5}+2q^{7}+q^{9}+2q^{12}+\cdots\)
6033.2.a.b 6033.a 1.a $71$ $48.174$ None \(-11\) \(71\) \(-8\) \(-46\) $-$ $-$ $\mathrm{SU}(2)$
6033.2.a.c 6033.a 1.a $82$ $48.174$ None \(13\) \(-82\) \(7\) \(30\) $+$ $-$ $\mathrm{SU}(2)$
6033.2.a.d 6033.a 1.a $84$ $48.174$ None \(-13\) \(-84\) \(-10\) \(-32\) $+$ $+$ $\mathrm{SU}(2)$
6033.2.a.e 6033.a 1.a $97$ $48.174$ None \(12\) \(97\) \(6\) \(50\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6033))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6033)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2011))\)\(^{\oplus 2}\)