Properties

Label 4033.2.a
Level 4033
Weight 2
Character orbit 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

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

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

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

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