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 $11$

Related objects

Downloads

Learn more

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 Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
576.4.a.a \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-18\) \(-8\) \(-\) \(-\) \(q-18q^{5}-8q^{7}-6^{2}q^{11}+10q^{13}+\cdots\)
576.4.a.b \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-18\) \(8\) \(+\) \(-\) \(q-18q^{5}+8q^{7}+6^{2}q^{11}+10q^{13}+\cdots\)
576.4.a.c \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-16\) \(-12\) \(+\) \(+\) \(q-2^{4}q^{5}-12q^{7}-2^{6}q^{11}-58q^{13}+\cdots\)
576.4.a.d \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-16\) \(12\) \(-\) \(+\) \(q-2^{4}q^{5}+12q^{7}+2^{6}q^{11}-58q^{13}+\cdots\)
576.4.a.e \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-14\) \(-36\) \(-\) \(-\) \(q-14q^{5}-6^{2}q^{7}-6^{2}q^{11}-54q^{13}+\cdots\)
576.4.a.f \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-14\) \(36\) \(-\) \(-\) \(q-14q^{5}+6^{2}q^{7}+6^{2}q^{11}-54q^{13}+\cdots\)
576.4.a.g \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-10\) \(-16\) \(+\) \(-\) \(q-10q^{5}-2^{4}q^{7}+40q^{11}+50q^{13}+\cdots\)
576.4.a.h \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-10\) \(16\) \(+\) \(-\) \(q-10q^{5}+2^{4}q^{7}-40q^{11}+50q^{13}+\cdots\)
576.4.a.i \(1\) \(33.985\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(q-4q^{5}-18q^{13}+104q^{17}-109q^{25}+\cdots\)
576.4.a.j \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-2\) \(-24\) \(-\) \(-\) \(q-2q^{5}-24q^{7}+44q^{11}-22q^{13}+\cdots\)
576.4.a.k \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(-2\) \(24\) \(+\) \(-\) \(q-2q^{5}+24q^{7}-44q^{11}-22q^{13}+\cdots\)
576.4.a.l \(1\) \(33.985\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-20\) \(-\) \(+\) \(q-20q^{7}+70q^{13}+56q^{19}-5^{3}q^{25}+\cdots\)
576.4.a.m \(1\) \(33.985\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(20\) \(+\) \(+\) \(q+20q^{7}+70q^{13}-56q^{19}-5^{3}q^{25}+\cdots\)
576.4.a.n \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(2\) \(-12\) \(-\) \(-\) \(q+2q^{5}-12q^{7}-60q^{11}+42q^{13}+\cdots\)
576.4.a.o \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(2\) \(12\) \(-\) \(-\) \(q+2q^{5}+12q^{7}+60q^{11}+42q^{13}+\cdots\)
576.4.a.p \(1\) \(33.985\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(-\) \(+\) \(q+4q^{5}-18q^{13}-104q^{17}-109q^{25}+\cdots\)
576.4.a.q \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(6\) \(-16\) \(+\) \(-\) \(q+6q^{5}-2^{4}q^{7}+12q^{11}-38q^{13}+\cdots\)
576.4.a.r \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(6\) \(16\) \(-\) \(-\) \(q+6q^{5}+2^{4}q^{7}-12q^{11}-38q^{13}+\cdots\)
576.4.a.s \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(10\) \(-4\) \(+\) \(-\) \(q+10q^{5}-4q^{7}+20q^{11}-70q^{13}+\cdots\)
576.4.a.t \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(10\) \(4\) \(+\) \(-\) \(q+10q^{5}+4q^{7}-20q^{11}-70q^{13}+\cdots\)
576.4.a.u \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(14\) \(-24\) \(+\) \(-\) \(q+14q^{5}-24q^{7}-28q^{11}+74q^{13}+\cdots\)
576.4.a.v \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(14\) \(24\) \(-\) \(-\) \(q+14q^{5}+24q^{7}+28q^{11}+74q^{13}+\cdots\)
576.4.a.w \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(16\) \(-12\) \(+\) \(+\) \(q+2^{4}q^{5}-12q^{7}+2^{6}q^{11}-58q^{13}+\cdots\)
576.4.a.x \(1\) \(33.985\) \(\Q\) None \(0\) \(0\) \(16\) \(12\) \(-\) \(+\) \(q+2^{4}q^{5}+12q^{7}-2^{6}q^{11}-58q^{13}+\cdots\)
576.4.a.y \(1\) \(33.985\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(22\) \(0\) \(-\) \(-\) \(q+22q^{5}+18q^{13}+94q^{17}+359q^{25}+\cdots\)
576.4.a.z \(2\) \(33.985\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q-\beta q^{5}+2\beta q^{7}-2^{5}q^{11}+14q^{13}+\cdots\)
576.4.a.ba \(2\) \(33.985\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q-\beta q^{5}-2\beta q^{7}+2^{5}q^{11}+14q^{13}+\cdots\)

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

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