Properties

Label 660.2.a
Level $660$
Weight $2$
Character orbit 660.a
Rep. character $\chi_{660}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $6$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 660.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(660))\).

Total New Old
Modular forms 156 8 148
Cusp forms 133 8 125
Eisenstein series 23 0 23

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

\(2\)\(3\)\(5\)\(11\)FrickeDim.
\(-\)\(+\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(6\)

Trace form

\( 8 q + 8 q^{9} + O(q^{10}) \) \( 8 q + 8 q^{9} + 8 q^{17} + 8 q^{19} + 8 q^{25} + 16 q^{29} - 4 q^{33} + 8 q^{35} + 8 q^{39} + 16 q^{47} + 24 q^{49} - 16 q^{51} + 8 q^{57} + 16 q^{59} + 16 q^{61} + 8 q^{65} - 16 q^{67} - 16 q^{71} + 8 q^{77} - 8 q^{79} + 8 q^{81} - 56 q^{83} + 8 q^{85} - 8 q^{87} + 32 q^{89} - 32 q^{91} - 32 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(660))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 11
660.2.a.a \(1\) \(5.270\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
660.2.a.b \(1\) \(5.270\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{9}+q^{11}-4q^{13}+q^{15}+\cdots\)
660.2.a.c \(1\) \(5.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-4q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
660.2.a.d \(1\) \(5.270\) \(\Q\) None \(0\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
660.2.a.e \(2\) \(5.270\) \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(2\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+q^{11}+\cdots\)
660.2.a.f \(2\) \(5.270\) \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(2\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}-q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(660))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(660)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 2}\)