Properties

Label 6040.2.a
Level 6040
Weight 2
Character orbit a
Rep. character \(\chi_{6040}(1,\cdot)\)
Character field \(\Q\)
Dimension 150
Newforms 19
Sturm bound 1824
Trace bound 11

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Defining parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)
Character field: \(\Q\)
Newforms: \( 19 \)
Sturm bound: \(1824\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6040))\).

Total New Old
Modular forms 920 150 770
Cusp forms 905 150 755
Eisenstein series 15 0 15

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

\(2\)\(5\)\(151\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(24\)
\(+\)\(+\)\(-\)\(-\)\(14\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(20\)
\(-\)\(+\)\(+\)\(-\)\(23\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(26\)
Plus space\(+\)\(71\)
Minus space\(-\)\(79\)

Trace form

\( 150q - 4q^{3} - 2q^{5} + 158q^{9} + O(q^{10}) \) \( 150q - 4q^{3} - 2q^{5} + 158q^{9} - 8q^{11} + 4q^{17} - 16q^{19} - 8q^{21} - 8q^{23} + 150q^{25} - 16q^{27} + 12q^{29} - 8q^{31} + 8q^{33} - 4q^{35} - 4q^{37} - 24q^{39} + 12q^{41} - 16q^{43} + 6q^{45} - 8q^{47} + 150q^{49} - 24q^{51} - 24q^{53} + 24q^{57} + 8q^{59} - 12q^{61} - 56q^{63} + 12q^{65} - 36q^{67} + 56q^{69} - 40q^{71} + 28q^{73} - 4q^{75} + 48q^{77} + 8q^{79} + 182q^{81} - 12q^{83} - 4q^{85} - 72q^{87} + 52q^{89} - 40q^{91} + 48q^{93} + 52q^{97} - 72q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6040))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 151
6040.2.a.a \(1\) \(48.230\) \(\Q\) None \(0\) \(-3\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(q-3q^{3}+q^{5}-4q^{7}+6q^{9}-q^{11}+\cdots\)
6040.2.a.b \(1\) \(48.230\) \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{3}-q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
6040.2.a.c \(1\) \(48.230\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(-\) \(-\) \(-\) \(q-q^{3}+q^{5}-4q^{7}-2q^{9}-5q^{11}+\cdots\)
6040.2.a.d \(1\) \(48.230\) \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-q^{7}-2q^{9}-q^{11}-q^{13}+\cdots\)
6040.2.a.e \(1\) \(48.230\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{5}-q^{7}-3q^{9}+5q^{11}-q^{13}+\cdots\)
6040.2.a.f \(1\) \(48.230\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(+\) \(+\) \(+\) \(q-q^{5}+2q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots\)
6040.2.a.g \(1\) \(48.230\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(q+q^{3}-q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots\)
6040.2.a.h \(1\) \(48.230\) \(\Q\) None \(0\) \(1\) \(1\) \(4\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+4q^{7}-2q^{9}-3q^{11}+\cdots\)
6040.2.a.i \(1\) \(48.230\) \(\Q\) None \(0\) \(1\) \(1\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}+q^{5}+4q^{7}-2q^{9}+4q^{11}+\cdots\)
6040.2.a.j \(1\) \(48.230\) \(\Q\) None \(0\) \(2\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
6040.2.a.k \(2\) \(48.230\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
6040.2.a.l \(9\) \(48.230\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(0\) \(9\) \(-2\) \(-\) \(-\) \(+\) \(q-\beta _{7}q^{3}+q^{5}+(\beta _{1}+\beta _{4})q^{7}-\beta _{5}q^{9}+\cdots\)
6040.2.a.m \(12\) \(48.230\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(-12\) \(5\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{3}-q^{5}+\beta _{9}q^{7}+(1-\beta _{3}+\beta _{10}+\cdots)q^{9}+\cdots\)
6040.2.a.n \(13\) \(48.230\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-4\) \(-13\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}-q^{5}-\beta _{7}q^{7}+\beta _{2}q^{9}+(-1+\cdots)q^{11}+\cdots\)
6040.2.a.o \(15\) \(48.230\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(5\) \(15\) \(7\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+q^{5}-\beta _{4}q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6040.2.a.p \(19\) \(48.230\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(-5\) \(19\) \(-8\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
6040.2.a.q \(23\) \(48.230\) None \(0\) \(-4\) \(-23\) \(-9\) \(+\) \(+\) \(+\)
6040.2.a.r \(23\) \(48.230\) None \(0\) \(2\) \(-23\) \(3\) \(-\) \(+\) \(+\)
6040.2.a.s \(24\) \(48.230\) None \(0\) \(2\) \(24\) \(3\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(151))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(302))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(604))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(755))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1510))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3020))\)\(^{\oplus 2}\)