Properties

Label 1344.2.a
Level $1344$
Weight $2$
Character orbit 1344.a
Rep. character $\chi_{1344}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $22$
Sturm bound $512$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(512\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1344))\).

Total New Old
Modular forms 280 24 256
Cusp forms 233 24 209
Eisenstein series 47 0 47

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

\(2\)\(3\)\(7\)FrickeDim
\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(4\)
\(+\)\(-\)\(-\)$+$\(1\)
\(-\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(5\)
Plus space\(+\)\(8\)
Minus space\(-\)\(16\)

Trace form

\( 24 q + 24 q^{9} + O(q^{10}) \) \( 24 q + 24 q^{9} + 16 q^{17} + 40 q^{25} + 16 q^{29} + 16 q^{37} + 16 q^{41} + 24 q^{49} + 16 q^{53} + 32 q^{61} + 32 q^{69} - 16 q^{73} + 16 q^{77} + 24 q^{81} + 32 q^{85} - 16 q^{89} + 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1344))\) 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 7
1344.2.a.a 1344.a 1.a $1$ $10.732$ \(\Q\) None 84.2.a.a \(0\) \(-1\) \(-4\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
1344.2.a.b 1344.a 1.a $1$ $10.732$ \(\Q\) None 168.2.a.a \(0\) \(-1\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}-6q^{13}+2q^{15}+\cdots\)
1344.2.a.c 1344.a 1.a $1$ $10.732$ \(\Q\) None 168.2.a.b \(0\) \(-1\) \(-2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
1344.2.a.d 1344.a 1.a $1$ $10.732$ \(\Q\) None 672.2.a.d \(0\) \(-1\) \(-2\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1344.2.a.e 1344.a 1.a $1$ $10.732$ \(\Q\) None 672.2.a.c \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.f 1344.a 1.a $1$ $10.732$ \(\Q\) None 84.2.a.b \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
1344.2.a.g 1344.a 1.a $1$ $10.732$ \(\Q\) None 21.2.a.a \(0\) \(-1\) \(2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
1344.2.a.h 1344.a 1.a $1$ $10.732$ \(\Q\) None 672.2.a.b \(0\) \(-1\) \(2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
1344.2.a.i 1344.a 1.a $1$ $10.732$ \(\Q\) None 42.2.a.a \(0\) \(-1\) \(2\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1344.2.a.j 1344.a 1.a $1$ $10.732$ \(\Q\) None 672.2.a.a \(0\) \(-1\) \(4\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.k 1344.a 1.a $1$ $10.732$ \(\Q\) None 84.2.a.a \(0\) \(1\) \(-4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
1344.2.a.l 1344.a 1.a $1$ $10.732$ \(\Q\) None 672.2.a.d \(0\) \(1\) \(-2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
1344.2.a.m 1344.a 1.a $1$ $10.732$ \(\Q\) None 168.2.a.a \(0\) \(1\) \(-2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}-6q^{13}-2q^{15}+\cdots\)
1344.2.a.n 1344.a 1.a $1$ $10.732$ \(\Q\) None 168.2.a.b \(0\) \(1\) \(-2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
1344.2.a.o 1344.a 1.a $1$ $10.732$ \(\Q\) None 84.2.a.b \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
1344.2.a.p 1344.a 1.a $1$ $10.732$ \(\Q\) None 672.2.a.c \(0\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.q 1344.a 1.a $1$ $10.732$ \(\Q\) None 42.2.a.a \(0\) \(1\) \(2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
1344.2.a.r 1344.a 1.a $1$ $10.732$ \(\Q\) None 672.2.a.b \(0\) \(1\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
1344.2.a.s 1344.a 1.a $1$ $10.732$ \(\Q\) None 21.2.a.a \(0\) \(1\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1344.2.a.t 1344.a 1.a $1$ $10.732$ \(\Q\) None 672.2.a.a \(0\) \(1\) \(4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.u 1344.a 1.a $2$ $10.732$ \(\Q(\sqrt{3}) \) None 672.2.a.i \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
1344.2.a.v 1344.a 1.a $2$ $10.732$ \(\Q(\sqrt{3}) \) None 672.2.a.i \(0\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1344))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1344)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 2}\)