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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11
264.2.a.a \(1\) \(2.108\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}+q^{11}+2q^{13}+\cdots\)
264.2.a.b \(1\) \(2.108\) \(\Q\) None \(0\) \(1\) \(-2\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}-2q^{5}+4q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
264.2.a.c \(1\) \(2.108\) \(\Q\) None \(0\) \(1\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{7}+q^{9}+q^{11}-2q^{17}+\cdots\)
264.2.a.d \(1\) \(2.108\) \(\Q\) None \(0\) \(1\) \(4\) \(-2\) \(+\) \(-\) \(+\) \(q+q^{3}+4q^{5}-2q^{7}+q^{9}-q^{11}+4q^{15}+\cdots\)

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))
$5$ (\( 1 - 2 T + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))
$7$ (\( 1 + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 2 T + 7 T^{2} \))
$11$ (\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( 1 + T \))
$13$ (\( 1 - 2 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))(\( 1 + 13 T^{2} \))(\( 1 + 13 T^{2} \))
$17$ (\( 1 - 6 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))
$19$ (\( 1 + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))
$23$ (\( 1 - 4 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 6 T + 23 T^{2} \))
$29$ (\( 1 - 2 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))(\( 1 - 6 T + 29 T^{2} \))
$31$ (\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))
$37$ (\( 1 + 10 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 + 10 T + 41 T^{2} \))
$43$ (\( 1 + 8 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 4 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))
$47$ (\( 1 + 4 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( 1 + 6 T + 47 T^{2} \))(\( 1 - 6 T + 47 T^{2} \))
$53$ (\( 1 + 6 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 8 T + 53 T^{2} \))(\( 1 + 12 T + 53 T^{2} \))
$59$ (\( 1 + 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))
$61$ (\( 1 - 2 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 + 4 T + 61 T^{2} \))(\( 1 - 4 T + 61 T^{2} \))
$67$ (\( 1 - 4 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 + 12 T + 67 T^{2} \))
$71$ (\( 1 - 12 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))(\( 1 + 10 T + 71 T^{2} \))(\( 1 - 10 T + 71 T^{2} \))
$73$ (\( 1 + 14 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))
$79$ (\( 1 - 16 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))(\( 1 + 10 T + 79 T^{2} \))(\( 1 - 2 T + 79 T^{2} \))
$83$ (\( 1 + 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 - 12 T + 83 T^{2} \))
$89$ (\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))
$97$ (\( 1 + 14 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))
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