Properties

Label 1584.2.a
Level $1584$
Weight $2$
Character orbit 1584.a
Rep. character $\chi_{1584}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $22$
Sturm bound $576$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(576\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1584))\).

Total New Old
Modular forms 312 25 287
Cusp forms 265 25 240
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.

\(2\)\(3\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(11\)
Minus space\(-\)\(14\)

Trace form

\( 25q - 2q^{5} - 4q^{7} + O(q^{10}) \) \( 25q - 2q^{5} - 4q^{7} - 3q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + 6q^{23} + 27q^{25} + 6q^{29} + 10q^{31} - 12q^{35} - 2q^{37} + 2q^{41} + 8q^{43} - 8q^{47} + 17q^{49} - 2q^{53} - 4q^{55} - 14q^{59} - 18q^{61} + 28q^{65} - 10q^{67} + 18q^{71} + 2q^{73} - 20q^{79} + 32q^{83} - 20q^{85} - 2q^{89} - 16q^{91} - 24q^{95} - 10q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11
1584.2.a.a \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(-4\) \(2\) \(+\) \(-\) \(+\) \(q-4q^{5}+2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
1584.2.a.b \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(-4\) \(2\) \(-\) \(+\) \(-\) \(q-4q^{5}+2q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
1584.2.a.c \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{5}-2q^{7}-q^{11}+6q^{13}+4q^{17}+\cdots\)
1584.2.a.d \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{5}+q^{11}+2q^{13}-6q^{17}+4q^{23}+\cdots\)
1584.2.a.e \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(-\) \(q-2q^{5}+2q^{7}+q^{11}-2q^{13}-4q^{17}+\cdots\)
1584.2.a.f \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(-2\) \(4\) \(-\) \(-\) \(+\) \(q-2q^{5}+4q^{7}-q^{11}-6q^{13}-2q^{17}+\cdots\)
1584.2.a.g \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(-\) \(q-q^{5}+2q^{7}+q^{11}+4q^{13}+2q^{17}+\cdots\)
1584.2.a.h \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(q-2q^{7}-q^{11}-4q^{13}+6q^{17}+4q^{19}+\cdots\)
1584.2.a.i \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-2q^{7}-q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\)
1584.2.a.j \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(q-2q^{7}+q^{11}+2q^{17}-8q^{19}-2q^{23}+\cdots\)
1584.2.a.k \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q-2q^{7}+q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\)
1584.2.a.l \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q+2q^{7}-q^{11}-6q^{13}-6q^{17}+2q^{19}+\cdots\)
1584.2.a.m \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+2q^{7}+q^{11}-6q^{13}+6q^{17}+2q^{19}+\cdots\)
1584.2.a.n \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(+\) \(-\) \(+\) \(q+2q^{5}-4q^{7}-q^{11}+6q^{13}-6q^{17}+\cdots\)
1584.2.a.o \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(-\) \(q+2q^{5}-4q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
1584.2.a.p \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(3\) \(-2\) \(-\) \(-\) \(+\) \(q+3q^{5}-2q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots\)
1584.2.a.q \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(3\) \(2\) \(+\) \(-\) \(+\) \(q+3q^{5}+2q^{7}-q^{11}+6q^{17}-4q^{19}+\cdots\)
1584.2.a.r \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(4\) \(2\) \(-\) \(+\) \(+\) \(q+4q^{5}+2q^{7}-q^{11}-2q^{13}-2q^{17}+\cdots\)
1584.2.a.s \(1\) \(12.648\) \(\Q\) None \(0\) \(0\) \(4\) \(2\) \(-\) \(-\) \(-\) \(q+4q^{5}+2q^{7}+q^{11}+4q^{13}+2q^{17}+\cdots\)
1584.2.a.t \(2\) \(12.648\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(2\) \(+\) \(-\) \(+\) \(q+(-1-\beta )q^{5}+(2-2\beta )q^{7}-q^{11}+\cdots\)
1584.2.a.u \(2\) \(12.648\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q+\beta q^{5}+(-2-\beta )q^{7}-q^{11}+(2-\beta )q^{13}+\cdots\)
1584.2.a.v \(2\) \(12.648\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q+\beta q^{5}+(-2+\beta )q^{7}+q^{11}+(2+\beta )q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1584))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1584)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 2}\)