Properties

Label 864.2.a
Level $864$
Weight $2$
Character orbit 864.a
Rep. character $\chi_{864}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $14$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(864))\).

Total New Old
Modular forms 168 16 152
Cusp forms 121 16 105
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.

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(10\)

Trace form

\( 16 q + O(q^{10}) \) \( 16 q + 8 q^{13} + 8 q^{25} + 40 q^{37} + 16 q^{49} + 40 q^{61} + 16 q^{85} + 32 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(864))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
864.2.a.a \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(-2\) \(-3\) \(-\) \(+\) \(q-2q^{5}-3q^{7}+6q^{11}-3q^{13}+2q^{17}+\cdots\)
864.2.a.b \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(q-2q^{5}-q^{7}+2q^{11}+q^{13}-6q^{17}+\cdots\)
864.2.a.c \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(-2\) \(1\) \(+\) \(+\) \(q-2q^{5}+q^{7}-2q^{11}+q^{13}-6q^{17}+\cdots\)
864.2.a.d \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(-2\) \(3\) \(-\) \(-\) \(q-2q^{5}+3q^{7}-6q^{11}-3q^{13}+2q^{17}+\cdots\)
864.2.a.e \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(+\) \(+\) \(q-q^{5}-3q^{7}+3q^{11}+4q^{17}-6q^{19}+\cdots\)
864.2.a.f \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(-1\) \(3\) \(+\) \(-\) \(q-q^{5}+3q^{7}-3q^{11}+4q^{17}+6q^{19}+\cdots\)
864.2.a.g \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(1\) \(-3\) \(-\) \(-\) \(q+q^{5}-3q^{7}-3q^{11}-4q^{17}-6q^{19}+\cdots\)
864.2.a.h \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(1\) \(3\) \(-\) \(+\) \(q+q^{5}+3q^{7}+3q^{11}-4q^{17}+6q^{19}+\cdots\)
864.2.a.i \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(2\) \(-3\) \(+\) \(+\) \(q+2q^{5}-3q^{7}-6q^{11}-3q^{13}-2q^{17}+\cdots\)
864.2.a.j \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(2\) \(-1\) \(+\) \(-\) \(q+2q^{5}-q^{7}-2q^{11}+q^{13}+6q^{17}+\cdots\)
864.2.a.k \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(2\) \(1\) \(-\) \(+\) \(q+2q^{5}+q^{7}+2q^{11}+q^{13}+6q^{17}+\cdots\)
864.2.a.l \(1\) \(6.899\) \(\Q\) None \(0\) \(0\) \(2\) \(3\) \(+\) \(-\) \(q+2q^{5}+3q^{7}+6q^{11}-3q^{13}-2q^{17}+\cdots\)
864.2.a.m \(2\) \(6.899\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q-\beta q^{5}+\beta q^{7}-q^{11}+4q^{13}-2\beta q^{19}+\cdots\)
864.2.a.n \(2\) \(6.899\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q-\beta q^{5}-\beta q^{7}+q^{11}+4q^{13}+2\beta q^{19}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(864))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(864)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 2}\)