Properties

Label 4015.2.a
Level 4015
Weight 2
Character orbit a
Rep. character \(\chi_{4015}(1,\cdot)\)
Character field \(\Q\)
Dimension 239
Newforms 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: \(\Q\)
Newforms: \( 9 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\) into irreducible Hecke orbits

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

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