Properties

Label 4015.2.a
Level 4015
Weight 2
Character orbit a
Rep. character \(\chi_{4015}(1,\cdot)\)
Character field \(\Q\)
Dimension 239
Newform subspaces 9
Sturm bound 888
Trace bound 2

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Defining parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(888\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4015))\).

Total New Old
Modular forms 448 239 209
Cusp forms 441 239 202
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)\(11\)\(73\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(32\)
\(+\)\(+\)\(-\)\(-\)\(27\)
\(+\)\(-\)\(+\)\(-\)\(27\)
\(+\)\(-\)\(-\)\(+\)\(32\)
\(-\)\(+\)\(+\)\(-\)\(38\)
\(-\)\(+\)\(-\)\(+\)\(23\)
\(-\)\(-\)\(+\)\(+\)\(23\)
\(-\)\(-\)\(-\)\(-\)\(37\)
Plus space\(+\)\(110\)
Minus space\(-\)\(129\)

Trace form

\( 239q - 3q^{2} - 4q^{3} + 241q^{4} + 3q^{5} + 4q^{6} - 8q^{7} - 15q^{8} + 235q^{9} + O(q^{10}) \) \( 239q - 3q^{2} - 4q^{3} + 241q^{4} + 3q^{5} + 4q^{6} - 8q^{7} - 15q^{8} + 235q^{9} + 5q^{10} - q^{11} + 12q^{12} - 14q^{13} + 24q^{14} + 4q^{15} + 233q^{16} - 18q^{17} + q^{18} - 4q^{19} + 5q^{20} + q^{22} - 16q^{23} + 28q^{24} + 239q^{25} + 6q^{26} - 40q^{27} - 16q^{28} + 2q^{29} - 4q^{30} + 17q^{32} + 4q^{33} + 2q^{34} + 205q^{36} - 22q^{37} - 12q^{38} - 56q^{39} + 33q^{40} - 18q^{41} - 24q^{42} - 4q^{43} - 7q^{44} + 23q^{45} + 64q^{46} + 8q^{47} - 44q^{48} + 231q^{49} - 3q^{50} + 56q^{51} - 98q^{52} - 22q^{53} + 32q^{54} - q^{55} + 24q^{56} - 32q^{57} - 26q^{58} - 36q^{59} - 4q^{60} + 2q^{61} + 16q^{62} - 24q^{63} + 241q^{64} - 14q^{65} - 12q^{66} - 20q^{67} + 2q^{68} + 32q^{69} - 48q^{71} - 3q^{72} - q^{73} + 62q^{74} - 4q^{75} - 68q^{76} - 8q^{77} + 40q^{78} - 32q^{79} - 3q^{80} + 231q^{81} + 10q^{82} + 52q^{83} + 80q^{84} + 22q^{85} - 44q^{86} - 56q^{87} - 3q^{88} + 54q^{89} + 65q^{90} - 64q^{91} + 16q^{92} - 80q^{93} - 24q^{94} - 4q^{95} + 12q^{96} - 18q^{97} - 131q^{98} - 13q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 11 73
4015.2.a.a \(1\) \(32.060\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}-q^{5}-3q^{7}-2q^{9}+q^{11}+\cdots\)
4015.2.a.b \(23\) \(32.060\) None \(-5\) \(-3\) \(23\) \(-10\) \(-\) \(-\) \(+\)
4015.2.a.c \(23\) \(32.060\) None \(-3\) \(-5\) \(23\) \(0\) \(-\) \(+\) \(-\)
4015.2.a.d \(27\) \(32.060\) None \(2\) \(3\) \(-27\) \(0\) \(+\) \(+\) \(-\)
4015.2.a.e \(27\) \(32.060\) None \(6\) \(5\) \(-27\) \(10\) \(+\) \(-\) \(+\)
4015.2.a.f \(31\) \(32.060\) None \(-7\) \(-4\) \(-31\) \(-11\) \(+\) \(-\) \(-\)
4015.2.a.g \(32\) \(32.060\) None \(-5\) \(-7\) \(-32\) \(0\) \(+\) \(+\) \(+\)
4015.2.a.h \(37\) \(32.060\) None \(5\) \(3\) \(37\) \(6\) \(-\) \(-\) \(-\)
4015.2.a.i \(38\) \(32.060\) None \(4\) \(5\) \(38\) \(0\) \(-\) \(+\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(73))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(365))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(803))\)\(^{\oplus 2}\)