Properties

Label 616.2.a
Level 616
Weight 2
Character orbit a
Rep. character \(\chi_{616}(1,\cdot)\)
Character field \(\Q\)
Dimension 14
Newforms 8
Sturm bound 192
Trace bound 5

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Defining parameters

Level: \( N \) = \( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 616.a (trivial)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(616))\).

Total New Old
Modular forms 104 14 90
Cusp forms 89 14 75
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.

\(2\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(9\)

Trace form

\( 14q + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 14q + 4q^{5} + 10q^{9} + 6q^{11} - 4q^{13} + 4q^{15} + 4q^{17} - 12q^{23} + 6q^{25} + 12q^{27} - 4q^{29} - 4q^{31} + 24q^{37} - 8q^{39} - 12q^{41} - 8q^{43} + 32q^{45} + 8q^{47} + 14q^{49} - 8q^{51} - 4q^{53} - 8q^{59} + 20q^{61} - 8q^{63} + 32q^{65} - 4q^{67} - 12q^{69} + 12q^{71} - 12q^{73} + 12q^{75} - 4q^{77} - 24q^{79} + 14q^{81} + 16q^{83} - 56q^{87} - 16q^{89} + 4q^{91} - 4q^{93} - 32q^{95} - 32q^{97} + 18q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(616))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 11
616.2.a.a \(1\) \(4.919\) \(\Q\) None \(0\) \(-2\) \(2\) \(1\) \(+\) \(-\) \(+\) \(q-2q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
616.2.a.b \(1\) \(4.919\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(-\) \(-\) \(q-q^{3}-q^{5}+q^{7}-2q^{9}+q^{11}+q^{15}+\cdots\)
616.2.a.c \(1\) \(4.919\) \(\Q\) None \(0\) \(0\) \(-2\) \(1\) \(-\) \(-\) \(+\) \(q-2q^{5}+q^{7}-3q^{9}-q^{11}+2q^{13}+\cdots\)
616.2.a.d \(1\) \(4.919\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{7}-3q^{9}-q^{11}-6q^{13}-2q^{19}+\cdots\)
616.2.a.e \(1\) \(4.919\) \(\Q\) None \(0\) \(2\) \(2\) \(1\) \(+\) \(-\) \(+\) \(q+2q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}+4q^{15}+\cdots\)
616.2.a.f \(2\) \(4.919\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-3\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta q^{3}+(-2+\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots\)
616.2.a.g \(3\) \(4.919\) 3.3.229.1 None \(0\) \(1\) \(1\) \(3\) \(-\) \(-\) \(-\) \(q-\beta _{2}q^{3}-\beta _{2}q^{5}+q^{7}+(1-\beta _{1})q^{9}+\cdots\)
616.2.a.h \(4\) \(4.919\) 4.4.11348.1 None \(0\) \(1\) \(5\) \(-4\) \(+\) \(+\) \(-\) \(q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(616))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(616)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 2}\)