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Properties

Label 264.4.a
Level $264$
Weight $4$
Character orbit 264.a
Rep. character $\chi_{264}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $9$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 264.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(264))\).

Total New Old
Modular forms 152 16 136
Cusp forms 136 16 120
Eisenstein series 16 0 16

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
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(10\)
Minus space\(-\)\(6\)

Trace form

\( 16 q - 6 q^{3} - 28 q^{5} + 36 q^{7} + 144 q^{9} + O(q^{10}) \) \( 16 q - 6 q^{3} - 28 q^{5} + 36 q^{7} + 144 q^{9} + 96 q^{13} - 172 q^{17} + 180 q^{19} + 60 q^{21} + 76 q^{23} + 488 q^{25} - 54 q^{27} + 556 q^{29} - 80 q^{31} + 66 q^{33} + 496 q^{35} + 72 q^{37} + 420 q^{39} + 324 q^{41} + 508 q^{43} - 252 q^{45} - 212 q^{47} + 936 q^{49} + 120 q^{51} + 1436 q^{53} - 84 q^{57} - 216 q^{59} - 56 q^{61} + 324 q^{63} + 56 q^{65} + 440 q^{67} + 252 q^{69} - 748 q^{71} - 136 q^{73} - 738 q^{75} - 476 q^{79} + 1296 q^{81} - 1136 q^{83} + 1512 q^{85} + 408 q^{87} - 2624 q^{89} - 2312 q^{91} + 1296 q^{93} - 3872 q^{95} + 1880 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(264))\) 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
264.4.a.a 264.a 1.a $1$ $15.577$ \(\Q\) None 264.4.a.a \(0\) \(-3\) \(-18\) \(-28\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-18q^{5}-28q^{7}+9q^{9}+11q^{11}+\cdots\)
264.4.a.b 264.a 1.a $1$ $15.577$ \(\Q\) None 264.4.a.b \(0\) \(-3\) \(12\) \(22\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+12q^{5}+22q^{7}+9q^{9}+11q^{11}+\cdots\)
264.4.a.c 264.a 1.a $1$ $15.577$ \(\Q\) None 264.4.a.c \(0\) \(3\) \(-6\) \(-14\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-6q^{5}-14q^{7}+9q^{9}+11q^{11}+\cdots\)
264.4.a.d 264.a 1.a $1$ $15.577$ \(\Q\) None 264.4.a.d \(0\) \(3\) \(-6\) \(-8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-6q^{5}-8q^{7}+9q^{9}-11q^{11}+\cdots\)
264.4.a.e 264.a 1.a $2$ $15.577$ \(\Q(\sqrt{17}) \) None 264.4.a.e \(0\) \(-6\) \(-6\) \(10\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-3-\beta )q^{5}+(5+\beta )q^{7}+9q^{9}+\cdots\)
264.4.a.f 264.a 1.a $2$ $15.577$ \(\Q(\sqrt{137}) \) None 264.4.a.f \(0\) \(-6\) \(-6\) \(16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-3-\beta )q^{5}+(8+2\beta )q^{7}+\cdots\)
264.4.a.g 264.a 1.a $2$ $15.577$ \(\Q(\sqrt{185}) \) None 264.4.a.g \(0\) \(6\) \(-6\) \(22\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-3-\beta )q^{5}+(11-\beta )q^{7}+\cdots\)
264.4.a.h 264.a 1.a $3$ $15.577$ 3.3.142161.1 None 264.4.a.h \(0\) \(-9\) \(4\) \(-12\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(1-\beta _{1})q^{5}+(-4+\beta _{2})q^{7}+\cdots\)
264.4.a.i 264.a 1.a $3$ $15.577$ 3.3.123209.1 None 264.4.a.i \(0\) \(9\) \(4\) \(28\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(1-\beta _{1})q^{5}+(10+\beta _{1}+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(264))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(264)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)