Properties

Label 576.4.a
Level $576$
Weight $4$
Character orbit 576.a
Rep. character $\chi_{576}(1,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $27$
Sturm bound $384$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(384\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(576))\).

Total New Old
Modular forms 312 31 281
Cusp forms 264 29 235
Eisenstein series 48 2 46

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

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(16\)
Minus space\(-\)\(13\)

Trace form

\( 29 q - 2 q^{5} + O(q^{10}) \) \( 29 q - 2 q^{5} - 70 q^{13} - 50 q^{17} + 667 q^{25} - 202 q^{29} + 498 q^{37} + 278 q^{41} + 1125 q^{49} - 34 q^{53} + 1994 q^{61} + 1020 q^{65} + 146 q^{73} + 2016 q^{77} + 1188 q^{85} + 806 q^{89} + 2394 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(576))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
576.4.a.a 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-18\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q-18q^{5}-8q^{7}-6^{2}q^{11}+10q^{13}+\cdots\)
576.4.a.b 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-18\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q-18q^{5}+8q^{7}+6^{2}q^{11}+10q^{13}+\cdots\)
576.4.a.c 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-16\) \(-12\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{5}-12q^{7}-2^{6}q^{11}-58q^{13}+\cdots\)
576.4.a.d 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-16\) \(12\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{5}+12q^{7}+2^{6}q^{11}-58q^{13}+\cdots\)
576.4.a.e 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-14\) \(-36\) $-$ $-$ $\mathrm{SU}(2)$ \(q-14q^{5}-6^{2}q^{7}-6^{2}q^{11}-54q^{13}+\cdots\)
576.4.a.f 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-14\) \(36\) $-$ $-$ $\mathrm{SU}(2)$ \(q-14q^{5}+6^{2}q^{7}+6^{2}q^{11}-54q^{13}+\cdots\)
576.4.a.g 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-10\) \(-16\) $+$ $-$ $\mathrm{SU}(2)$ \(q-10q^{5}-2^{4}q^{7}+40q^{11}+50q^{13}+\cdots\)
576.4.a.h 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-10\) \(16\) $+$ $-$ $\mathrm{SU}(2)$ \(q-10q^{5}+2^{4}q^{7}-40q^{11}+50q^{13}+\cdots\)
576.4.a.i 576.a 1.a $1$ $33.985$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-4q^{5}-18q^{13}+104q^{17}-109q^{25}+\cdots\)
576.4.a.j 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-2\) \(-24\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-24q^{7}+44q^{11}-22q^{13}+\cdots\)
576.4.a.k 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(-2\) \(24\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+24q^{7}-44q^{11}-22q^{13}+\cdots\)
576.4.a.l 576.a 1.a $1$ $33.985$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-20\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-20q^{7}+70q^{13}+56q^{19}-5^{3}q^{25}+\cdots\)
576.4.a.m 576.a 1.a $1$ $33.985$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(20\) $+$ $+$ $N(\mathrm{U}(1))$ \(q+20q^{7}+70q^{13}-56q^{19}-5^{3}q^{25}+\cdots\)
576.4.a.n 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(2\) \(-12\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-12q^{7}-60q^{11}+42q^{13}+\cdots\)
576.4.a.o 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(2\) \(12\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+12q^{7}+60q^{11}+42q^{13}+\cdots\)
576.4.a.p 576.a 1.a $1$ $33.985$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+4q^{5}-18q^{13}-104q^{17}-109q^{25}+\cdots\)
576.4.a.q 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(6\) \(-16\) $+$ $-$ $\mathrm{SU}(2)$ \(q+6q^{5}-2^{4}q^{7}+12q^{11}-38q^{13}+\cdots\)
576.4.a.r 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(6\) \(16\) $-$ $-$ $\mathrm{SU}(2)$ \(q+6q^{5}+2^{4}q^{7}-12q^{11}-38q^{13}+\cdots\)
576.4.a.s 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(10\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+10q^{5}-4q^{7}+20q^{11}-70q^{13}+\cdots\)
576.4.a.t 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(10\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+10q^{5}+4q^{7}-20q^{11}-70q^{13}+\cdots\)
576.4.a.u 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(14\) \(-24\) $+$ $-$ $\mathrm{SU}(2)$ \(q+14q^{5}-24q^{7}-28q^{11}+74q^{13}+\cdots\)
576.4.a.v 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(14\) \(24\) $-$ $-$ $\mathrm{SU}(2)$ \(q+14q^{5}+24q^{7}+28q^{11}+74q^{13}+\cdots\)
576.4.a.w 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(16\) \(-12\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{5}-12q^{7}+2^{6}q^{11}-58q^{13}+\cdots\)
576.4.a.x 576.a 1.a $1$ $33.985$ \(\Q\) None \(0\) \(0\) \(16\) \(12\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{5}+12q^{7}-2^{6}q^{11}-58q^{13}+\cdots\)
576.4.a.y 576.a 1.a $1$ $33.985$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(22\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q+22q^{5}+18q^{13}+94q^{17}+359q^{25}+\cdots\)
576.4.a.z 576.a 1.a $2$ $33.985$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+2\beta q^{7}-2^{5}q^{11}+14q^{13}+\cdots\)
576.4.a.ba 576.a 1.a $2$ $33.985$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-2\beta q^{7}+2^{5}q^{11}+14q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(576))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(576)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)