Properties

Label 4033.2.a
Level 4033
Weight 2
Character orbit a
Rep. character \(\chi_{4033}(1,\cdot)\)
Character field \(\Q\)
Dimension 325
Newforms 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: \(\Q\)
Newforms: \( 6 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4033))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 37 109
4033.2.a.a \(1\) \(32.204\) \(\Q\) None \(-1\) \(0\) \(2\) \(0\) \(+\) \(+\) \(q-q^{2}-q^{4}+2q^{5}+3q^{8}-3q^{9}-2q^{10}+\cdots\)
4033.2.a.b \(1\) \(32.204\) \(\Q\) None \(1\) \(0\) \(-2\) \(2\) \(+\) \(-\) \(q+q^{2}-q^{4}-2q^{5}+2q^{7}-3q^{8}-3q^{9}+\cdots\)
4033.2.a.c \(77\) \(32.204\) None \(-9\) \(-27\) \(-16\) \(-23\) \(-\) \(-\)
4033.2.a.d \(79\) \(32.204\) None \(-11\) \(-11\) \(-16\) \(-15\) \(+\) \(+\)
4033.2.a.e \(82\) \(32.204\) None \(10\) \(17\) \(22\) \(15\) \(+\) \(-\)
4033.2.a.f \(85\) \(32.204\) None \(11\) \(21\) \(12\) \(17\) \(-\) \(+\)

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

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