Properties

Label 4033.2.a
Level $4033$
Weight $2$
Character orbit 4033.a
Rep. character $\chi_{4033}(1,\cdot)$
Character field $\Q$
Dimension $325$
Newform subspaces $6$
Sturm bound $696$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 4033 = 37 \cdot 109 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4033.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(696\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4033))\).

Total New Old
Modular forms 348 325 23
Cusp forms 345 325 20
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.

\(37\)\(109\)FrickeDim
\(+\)\(+\)$+$\(80\)
\(+\)\(-\)$-$\(83\)
\(-\)\(+\)$-$\(85\)
\(-\)\(-\)$+$\(77\)
Plus space\(+\)\(157\)
Minus space\(-\)\(168\)

Trace form

\( 325 q + q^{2} + 331 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} - 3 q^{8} + 325 q^{9} + O(q^{10}) \) \( 325 q + q^{2} + 331 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} - 3 q^{8} + 325 q^{9} - 6 q^{10} + 4 q^{11} - 12 q^{12} + 2 q^{13} - 8 q^{14} - 20 q^{15} + 323 q^{16} - 26 q^{17} - 15 q^{18} - 8 q^{19} - 10 q^{20} + 4 q^{21} - 28 q^{22} - 28 q^{23} + 12 q^{24} + 311 q^{25} - 42 q^{26} - 12 q^{27} - 20 q^{28} + 14 q^{29} - 16 q^{30} + 24 q^{31} - 55 q^{32} - 40 q^{33} + 10 q^{34} + 8 q^{35} + 335 q^{36} - q^{37} + 24 q^{38} - 18 q^{40} + 6 q^{41} - 20 q^{42} - 56 q^{43} - 4 q^{44} + 26 q^{45} + 32 q^{46} + 20 q^{47} - 32 q^{48} + 329 q^{49} - 33 q^{50} - 12 q^{51} - 34 q^{52} - 2 q^{53} - 16 q^{54} - 92 q^{55} - 32 q^{56} - 48 q^{57} - 26 q^{58} - 56 q^{59} - 24 q^{60} + 6 q^{61} - 28 q^{62} - 40 q^{63} + 351 q^{64} - 36 q^{65} + 64 q^{66} - 34 q^{68} - 4 q^{69} + 4 q^{70} - 4 q^{71} - 75 q^{72} - 70 q^{73} + 3 q^{74} - 32 q^{75} + 32 q^{76} - 48 q^{77} + 92 q^{78} + 12 q^{79} - 2 q^{80} + 317 q^{81} - 38 q^{82} - 20 q^{83} - 28 q^{84} - 68 q^{86} + 24 q^{87} - 64 q^{88} + 70 q^{89} + 66 q^{90} + 36 q^{91} - 72 q^{92} - 12 q^{93} - 20 q^{94} - 36 q^{95} - 4 q^{96} + 2 q^{97} + 5 q^{98} + 60 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4033))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 37 109
4033.2.a.a 4033.a 1.a $1$ $32.204$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots\)
4033.2.a.b 4033.a 1.a $1$ $32.204$ \(\Q\) None \(1\) \(0\) \(-2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}+2q^{7}-3q^{8}-3q^{9}+\cdots\)
4033.2.a.c 4033.a 1.a $77$ $32.204$ None \(-9\) \(-27\) \(-16\) \(-23\) $-$ $-$ $\mathrm{SU}(2)$
4033.2.a.d 4033.a 1.a $79$ $32.204$ None \(-11\) \(-11\) \(-16\) \(-15\) $+$ $+$ $\mathrm{SU}(2)$
4033.2.a.e 4033.a 1.a $82$ $32.204$ None \(10\) \(17\) \(22\) \(15\) $+$ $-$ $\mathrm{SU}(2)$
4033.2.a.f 4033.a 1.a $85$ $32.204$ None \(11\) \(21\) \(12\) \(17\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4033))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4033)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(109))\)\(^{\oplus 2}\)