Properties

Label 264.2.a
Level $264$
Weight $2$
Character orbit 264.a
Rep. character $\chi_{264}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 264.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(264))\).

Total New Old
Modular forms 56 4 52
Cusp forms 41 4 37
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.

\(2\)\(3\)\(11\)FrickeDim
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(4\)

Trace form

\( 4 q + 2 q^{3} + 4 q^{5} + 4 q^{7} + 4 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} + 4 q^{5} + 4 q^{7} + 4 q^{9} + 8 q^{13} + 4 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{23} + 4 q^{25} + 2 q^{27} - 4 q^{29} - 2 q^{33} - 16 q^{35} + 4 q^{39} - 12 q^{41} - 20 q^{43} + 4 q^{45} - 4 q^{47} - 4 q^{49} - 8 q^{51} - 20 q^{53} + 4 q^{57} - 24 q^{59} + 4 q^{63} - 8 q^{65} - 8 q^{67} - 12 q^{69} + 4 q^{71} - 16 q^{73} + 6 q^{75} + 4 q^{79} + 4 q^{81} - 16 q^{83} - 24 q^{85} - 8 q^{87} + 8 q^{89} + 24 q^{91} + 32 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(264))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 11
264.2.a.a 264.a 1.a $1$ $2.108$ \(\Q\) None 264.2.a.a \(0\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}+q^{11}+2q^{13}+\cdots\)
264.2.a.b 264.a 1.a $1$ $2.108$ \(\Q\) None 264.2.a.b \(0\) \(1\) \(-2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+4q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
264.2.a.c 264.a 1.a $1$ $2.108$ \(\Q\) None 264.2.a.c \(0\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+q^{11}-2q^{17}+\cdots\)
264.2.a.d 264.a 1.a $1$ $2.108$ \(\Q\) None 264.2.a.d \(0\) \(1\) \(4\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}-2q^{7}+q^{9}-q^{11}+4q^{15}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(264))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(264)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)