Properties

Label 4034.2.a
Level 4034
Weight 2
Character orbit a
Rep. character \(\chi_{4034}(1,\cdot)\)
Character field \(\Q\)
Dimension 169
Newforms 4
Sturm bound 1009
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4034.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(1009\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4034))\).

Total New Old
Modular forms 506 169 337
Cusp forms 503 169 334
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.

\(2\)\(2017\)FrickeDim.
\(+\)\(+\)\(+\)\(35\)
\(+\)\(-\)\(-\)\(49\)
\(-\)\(+\)\(-\)\(52\)
\(-\)\(-\)\(+\)\(33\)
Plus space\(+\)\(68\)
Minus space\(-\)\(101\)

Trace form

\(169q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 169q^{4} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 169q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(169q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 169q^{4} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 169q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 169q^{16} \) \(\mathstrut -\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 179q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 18q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut +\mathstrut 20q^{33} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 169q^{36} \) \(\mathstrut +\mathstrut 32q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 8q^{44} \) \(\mathstrut +\mathstrut 20q^{45} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 169q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut 24q^{51} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 4q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut +\mathstrut 40q^{63} \) \(\mathstrut +\mathstrut 169q^{64} \) \(\mathstrut +\mathstrut 36q^{65} \) \(\mathstrut +\mathstrut 24q^{66} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 5q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut +\mathstrut 32q^{75} \) \(\mathstrut +\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 20q^{78} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 185q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut +\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 4q^{84} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut +\mathstrut 18q^{86} \) \(\mathstrut -\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 8q^{88} \) \(\mathstrut +\mathstrut 30q^{89} \) \(\mathstrut -\mathstrut 8q^{90} \) \(\mathstrut +\mathstrut 20q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 40q^{93} \) \(\mathstrut -\mathstrut 12q^{94} \) \(\mathstrut -\mathstrut 92q^{95} \) \(\mathstrut +\mathstrut 30q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut -\mathstrut 60q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4034))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 2017
4034.2.a.a \(33\) \(32.212\) None \(33\) \(-14\) \(-22\) \(-12\) \(-\) \(-\)
4034.2.a.b \(35\) \(32.212\) None \(-35\) \(-6\) \(6\) \(-14\) \(+\) \(+\)
4034.2.a.c \(49\) \(32.212\) None \(-49\) \(8\) \(-8\) \(18\) \(+\) \(-\)
4034.2.a.d \(52\) \(32.212\) None \(52\) \(16\) \(24\) \(12\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4034))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4034)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2017))\)\(^{\oplus 2}\)