Properties

Label 288.2.a
Level $288$
Weight $2$
Character orbit 288.a
Rep. character $\chi_{288}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(288))\).

Total New Old
Modular forms 64 5 59
Cusp forms 33 5 28
Eisenstein series 31 0 31

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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(3\)

Trace form

\( 5q - 2q^{5} + O(q^{10}) \) \( 5q - 2q^{5} - 10q^{13} + 10q^{17} + 19q^{25} + 6q^{29} - 10q^{37} - 14q^{41} - 3q^{49} - 34q^{53} - 18q^{61} + 20q^{65} - 6q^{73} + 32q^{77} + 36q^{85} - 30q^{89} - 46q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(288))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
288.2.a.a \(1\) \(2.300\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(+\) \(+\) \(q-4q^{5}-6q^{13}-8q^{17}+11q^{25}+\cdots\)
288.2.a.b \(1\) \(2.300\) \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) \(-\) \(-\) \(q-2q^{5}-4q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
288.2.a.c \(1\) \(2.300\) \(\Q\) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(-\) \(q-2q^{5}+4q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
288.2.a.d \(1\) \(2.300\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(q+2q^{5}+6q^{13}-2q^{17}-q^{25}+10q^{29}+\cdots\)
288.2.a.e \(1\) \(2.300\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(-\) \(+\) \(q+4q^{5}-6q^{13}+8q^{17}+11q^{25}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(288))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(288)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)