Properties

Label 4031.2.a
Level 4031
Weight 2
Character orbit a
Rep. character \(\chi_{4031}(1,\cdot)\)
Character field \(\Q\)
Dimension 323
Newforms 5
Sturm bound 700
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(700\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4031))\).

Total New Old
Modular forms 352 323 29
Cusp forms 349 323 26
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.

\(29\)\(139\)FrickeDim.
\(+\)\(+\)\(+\)\(61\)
\(+\)\(-\)\(-\)\(103\)
\(-\)\(+\)\(-\)\(100\)
\(-\)\(-\)\(+\)\(59\)
Plus space\(+\)\(120\)
Minus space\(-\)\(203\)

Trace form

\(323q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 329q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 331q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(323q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 329q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 331q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut +\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 337q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 22q^{20} \) \(\mathstrut +\mathstrut 32q^{21} \) \(\mathstrut +\mathstrut 16q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut +\mathstrut 40q^{24} \) \(\mathstrut +\mathstrut 341q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 44q^{28} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 60q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 357q^{36} \) \(\mathstrut +\mathstrut 22q^{37} \) \(\mathstrut -\mathstrut 32q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 36q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 28q^{44} \) \(\mathstrut -\mathstrut 58q^{45} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut -\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut 48q^{48} \) \(\mathstrut +\mathstrut 379q^{49} \) \(\mathstrut -\mathstrut 39q^{50} \) \(\mathstrut +\mathstrut 8q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut -\mathstrut 26q^{53} \) \(\mathstrut +\mathstrut 36q^{54} \) \(\mathstrut +\mathstrut 28q^{55} \) \(\mathstrut -\mathstrut 32q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 20q^{60} \) \(\mathstrut +\mathstrut 50q^{61} \) \(\mathstrut +\mathstrut 32q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 405q^{64} \) \(\mathstrut +\mathstrut 20q^{65} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 16q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 24q^{69} \) \(\mathstrut -\mathstrut 36q^{70} \) \(\mathstrut -\mathstrut 32q^{71} \) \(\mathstrut -\mathstrut 13q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 60q^{76} \) \(\mathstrut +\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 108q^{78} \) \(\mathstrut +\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 18q^{80} \) \(\mathstrut +\mathstrut 355q^{81} \) \(\mathstrut -\mathstrut 90q^{82} \) \(\mathstrut -\mathstrut 40q^{83} \) \(\mathstrut +\mathstrut 100q^{84} \) \(\mathstrut +\mathstrut 60q^{85} \) \(\mathstrut +\mathstrut 4q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 72q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 34q^{90} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut -\mathstrut 96q^{92} \) \(\mathstrut -\mathstrut 44q^{93} \) \(\mathstrut +\mathstrut 28q^{94} \) \(\mathstrut +\mathstrut 8q^{95} \) \(\mathstrut +\mathstrut 44q^{96} \) \(\mathstrut +\mathstrut 70q^{97} \) \(\mathstrut +\mathstrut 19q^{98} \) \(\mathstrut +\mathstrut 80q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4031))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 29 139
4031.2.a.a \(2\) \(32.188\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(4\) \(-2\) \(-\) \(+\) \(q+(1+\beta )q^{2}+(1+\beta )q^{3}+(1+2\beta )q^{4}+\cdots\)
4031.2.a.b \(59\) \(32.188\) None \(-5\) \(-6\) \(-5\) \(-10\) \(-\) \(-\)
4031.2.a.c \(61\) \(32.188\) None \(-1\) \(-4\) \(-7\) \(-10\) \(+\) \(+\)
4031.2.a.d \(98\) \(32.188\) None \(6\) \(6\) \(1\) \(12\) \(-\) \(+\)
4031.2.a.e \(103\) \(32.188\) None \(1\) \(2\) \(9\) \(18\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4031))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4031)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(139))\)\(^{\oplus 2}\)