Properties

Label 2664.2.a
Level $2664$
Weight $2$
Character orbit 2664.a
Rep. character $\chi_{2664}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $20$
Sturm bound $912$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2664.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(912\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2664))\).

Total New Old
Modular forms 472 45 427
Cusp forms 441 45 396
Eisenstein series 31 0 31

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

\(2\)\(3\)\(37\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(8\)
Plus space\(+\)\(20\)
Minus space\(-\)\(25\)

Trace form

\( 45 q - 2 q^{5} - 4 q^{7} + O(q^{10}) \) \( 45 q - 2 q^{5} - 4 q^{7} - 2 q^{11} + 2 q^{13} + 6 q^{17} - 16 q^{23} + 57 q^{25} + 10 q^{29} + q^{37} + 4 q^{41} - 8 q^{43} - 8 q^{47} + 73 q^{49} - 18 q^{53} + 16 q^{55} - 8 q^{59} - 2 q^{61} + 24 q^{65} + 6 q^{67} + 28 q^{71} - 28 q^{73} + 16 q^{77} - 4 q^{79} - 16 q^{83} - 28 q^{85} - 6 q^{89} - 28 q^{91} + 20 q^{95} - 10 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2664))\) 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 37
2664.2.a.a 2664.a 1.a $1$ $21.272$ \(\Q\) None 888.2.a.d \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{13}+6q^{23}+11q^{25}+\cdots\)
2664.2.a.b 2664.a 1.a $1$ $21.272$ \(\Q\) None 2664.2.a.b \(0\) \(0\) \(-2\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-5q^{11}+3q^{13}-q^{17}+\cdots\)
2664.2.a.c 2664.a 1.a $1$ $21.272$ \(\Q\) None 296.2.a.b \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{7}+3q^{11}-2q^{17}-2q^{19}+6q^{23}+\cdots\)
2664.2.a.d 2664.a 1.a $1$ $21.272$ \(\Q\) None 888.2.a.b \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-6q^{13}+4q^{17}+4q^{19}-6q^{23}+\cdots\)
2664.2.a.e 2664.a 1.a $1$ $21.272$ \(\Q\) None 888.2.a.c \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{11}-2q^{13}+6q^{17}+4q^{23}+\cdots\)
2664.2.a.f 2664.a 1.a $1$ $21.272$ \(\Q\) None 296.2.a.a \(0\) \(0\) \(2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-q^{11}-6q^{13}+4q^{17}+\cdots\)
2664.2.a.g 2664.a 1.a $1$ $21.272$ \(\Q\) None 2664.2.a.b \(0\) \(0\) \(2\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+5q^{11}+3q^{13}+q^{17}+\cdots\)
2664.2.a.h 2664.a 1.a $1$ $21.272$ \(\Q\) None 888.2.a.a \(0\) \(0\) \(4\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}+3q^{11}-5q^{13}-7q^{17}+\cdots\)
2664.2.a.i 2664.a 1.a $2$ $21.272$ \(\Q(\sqrt{3}) \) None 888.2.a.e \(0\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}-2q^{7}+(2-2\beta )q^{11}+\cdots\)
2664.2.a.j 2664.a 1.a $2$ $21.272$ \(\Q(\sqrt{5}) \) None 888.2.a.f \(0\) \(0\) \(-2\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+4q^{7}+(-2-2\beta )q^{11}+\cdots\)
2664.2.a.k 2664.a 1.a $2$ $21.272$ \(\Q(\sqrt{41}) \) None 888.2.a.h \(0\) \(0\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{7}+(-1-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
2664.2.a.l 2664.a 1.a $2$ $21.272$ \(\Q(\sqrt{2}) \) None 888.2.a.g \(0\) \(0\) \(4\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(-2+2\beta )q^{7}+2\beta q^{11}+\cdots\)
2664.2.a.m 2664.a 1.a $3$ $21.272$ 3.3.316.1 None 888.2.a.i \(0\) \(0\) \(-2\) \(-5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots\)
2664.2.a.n 2664.a 1.a $3$ $21.272$ 3.3.148.1 None 2664.2.a.n \(0\) \(0\) \(-2\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2664.2.a.o 2664.a 1.a $3$ $21.272$ 3.3.568.1 None 888.2.a.j \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{2})q^{11}+\cdots\)
2664.2.a.p 2664.a 1.a $3$ $21.272$ 3.3.229.1 None 296.2.a.c \(0\) \(0\) \(1\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+3\beta _{1}q^{11}+\cdots\)
2664.2.a.q 2664.a 1.a $3$ $21.272$ 3.3.148.1 None 2664.2.a.n \(0\) \(0\) \(2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{5}+(2-\beta _{1}-\beta _{2})q^{7}-2q^{13}+\cdots\)
2664.2.a.r 2664.a 1.a $4$ $21.272$ 4.4.48389.1 None 296.2.a.d \(0\) \(0\) \(-5\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{5}+(-\beta _{2}+\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots\)
2664.2.a.s 2664.a 1.a $5$ $21.272$ 5.5.935504.1 None 2664.2.a.s \(0\) \(0\) \(-2\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+(-1+\beta _{4})q^{7}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)
2664.2.a.t 2664.a 1.a $5$ $21.272$ 5.5.935504.1 None 2664.2.a.s \(0\) \(0\) \(2\) \(-7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(-1+\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2664)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(333))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(666))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(888))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1332))\)\(^{\oplus 2}\)