Properties

Label 1152.2.a
Level $1152$
Weight $2$
Character orbit 1152.a
Rep. character $\chi_{1152}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $20$
Sturm bound $384$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(384\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1152))\).

Total New Old
Modular forms 224 20 204
Cusp forms 161 20 141
Eisenstein series 63 0 63

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

\(2\)\(3\)FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(+\)\(+\)\(52\)\(4\)\(48\)\(37\)\(4\)\(33\)\(15\)\(0\)\(15\)
\(+\)\(-\)\(-\)\(56\)\(7\)\(49\)\(40\)\(7\)\(33\)\(16\)\(0\)\(16\)
\(-\)\(+\)\(-\)\(60\)\(4\)\(56\)\(44\)\(4\)\(40\)\(16\)\(0\)\(16\)
\(-\)\(-\)\(+\)\(56\)\(5\)\(51\)\(40\)\(5\)\(35\)\(16\)\(0\)\(16\)
Plus space\(+\)\(108\)\(9\)\(99\)\(77\)\(9\)\(68\)\(31\)\(0\)\(31\)
Minus space\(-\)\(116\)\(11\)\(105\)\(84\)\(11\)\(73\)\(32\)\(0\)\(32\)

Trace form

\( 20 q - 8 q^{17} + 12 q^{25} + 8 q^{41} - 12 q^{49} + 16 q^{65} - 8 q^{73} + 56 q^{89} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1152))\) 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
1152.2.a.a 1152.a 1.a $1$ $9.199$ \(\Q\) None 384.2.a.a \(0\) \(0\) \(-4\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-2q^{7}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.b 1152.a 1.a $1$ $9.199$ \(\Q\) None 384.2.a.a \(0\) \(0\) \(-4\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{7}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.c 1152.a 1.a $1$ $9.199$ \(\Q\) None 128.2.a.a \(0\) \(0\) \(-2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}+2q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.a.d 1152.a 1.a $1$ $9.199$ \(\Q\) None 1152.2.a.d \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}+4q^{11}-2q^{13}+4q^{17}+\cdots\)
1152.2.a.e 1152.a 1.a $1$ $9.199$ \(\Q\) None 1152.2.a.d \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}+4q^{11}+2q^{13}-4q^{17}+\cdots\)
1152.2.a.f 1152.a 1.a $1$ $9.199$ \(\Q\) None 1152.2.a.d \(0\) \(0\) \(-2\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-4q^{11}-2q^{13}+4q^{17}+\cdots\)
1152.2.a.g 1152.a 1.a $1$ $9.199$ \(\Q\) None 1152.2.a.d \(0\) \(0\) \(-2\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-4q^{11}+2q^{13}-4q^{17}+\cdots\)
1152.2.a.h 1152.a 1.a $1$ $9.199$ \(\Q\) None 128.2.a.a \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{7}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.a.i 1152.a 1.a $1$ $9.199$ \(\Q\) None 384.2.a.b \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-4q^{11}+6q^{13}-6q^{17}+4q^{23}+\cdots\)
1152.2.a.j 1152.a 1.a $1$ $9.199$ \(\Q\) None 384.2.a.b \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+4q^{11}-6q^{13}-6q^{17}+4q^{23}+\cdots\)
1152.2.a.k 1152.a 1.a $1$ $9.199$ \(\Q\) None 384.2.a.b \(0\) \(0\) \(0\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-4q^{11}-6q^{13}-6q^{17}-4q^{23}+\cdots\)
1152.2.a.l 1152.a 1.a $1$ $9.199$ \(\Q\) None 384.2.a.b \(0\) \(0\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+4q^{11}+6q^{13}-6q^{17}-4q^{23}+\cdots\)
1152.2.a.m 1152.a 1.a $1$ $9.199$ \(\Q\) None 128.2.a.a \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.n 1152.a 1.a $1$ $9.199$ \(\Q\) None 1152.2.a.d \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-4q^{11}-2q^{13}-4q^{17}+\cdots\)
1152.2.a.o 1152.a 1.a $1$ $9.199$ \(\Q\) None 1152.2.a.d \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-4q^{11}+2q^{13}+4q^{17}+\cdots\)
1152.2.a.p 1152.a 1.a $1$ $9.199$ \(\Q\) None 1152.2.a.d \(0\) \(0\) \(2\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+4q^{11}-2q^{13}-4q^{17}+\cdots\)
1152.2.a.q 1152.a 1.a $1$ $9.199$ \(\Q\) None 1152.2.a.d \(0\) \(0\) \(2\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+4q^{11}+2q^{13}+4q^{17}+\cdots\)
1152.2.a.r 1152.a 1.a $1$ $9.199$ \(\Q\) None 128.2.a.a \(0\) \(0\) \(2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.s 1152.a 1.a $1$ $9.199$ \(\Q\) None 384.2.a.a \(0\) \(0\) \(4\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-2q^{7}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.a.t 1152.a 1.a $1$ $9.199$ \(\Q\) None 384.2.a.a \(0\) \(0\) \(4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+2q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1152))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1152)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)