Properties

Label 4034.2.a
Level 4034
Weight 2
Character orbit a
Rep. character \(\chi_{4034}(1,\cdot)\)
Character field \(\Q\)
Dimension 169
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4034))\) into newform subspaces

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

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