Properties

Label 144.4.a
Level $144$
Weight $4$
Character orbit 144.a
Rep. character $\chi_{144}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $7$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 144.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(144))\).

Total New Old
Modular forms 84 8 76
Cusp forms 60 7 53
Eisenstein series 24 1 23

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.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(3\)

Trace form

\( 7q + 12q^{7} + O(q^{10}) \) \( 7q + 12q^{7} - 24q^{11} + 22q^{13} - 24q^{17} + 160q^{19} + 192q^{23} + 197q^{25} + 144q^{29} - 164q^{31} - 624q^{35} - 30q^{37} - 216q^{41} + 464q^{43} + 1104q^{47} - 241q^{49} - 240q^{53} - 1168q^{55} - 1416q^{59} - 518q^{61} + 672q^{65} + 904q^{67} + 2016q^{71} - 614q^{73} + 288q^{77} - 2404q^{79} - 2952q^{83} + 992q^{85} - 648q^{89} + 1176q^{91} + 3120q^{95} - 430q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(144))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
144.4.a.a \(1\) \(8.496\) \(\Q\) None \(0\) \(0\) \(-16\) \(12\) \(+\) \(+\) \(q-2^{4}q^{5}+12q^{7}+2^{6}q^{11}+58q^{13}+\cdots\)
144.4.a.b \(1\) \(8.496\) \(\Q\) None \(0\) \(0\) \(-14\) \(24\) \(+\) \(-\) \(q-14q^{5}+24q^{7}-28q^{11}-74q^{13}+\cdots\)
144.4.a.c \(1\) \(8.496\) \(\Q\) None \(0\) \(0\) \(-6\) \(16\) \(-\) \(-\) \(q-6q^{5}+2^{4}q^{7}+12q^{11}+38q^{13}+\cdots\)
144.4.a.d \(1\) \(8.496\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-20\) \(-\) \(+\) \(q-20q^{7}-70q^{13}-56q^{19}-5^{3}q^{25}+\cdots\)
144.4.a.e \(1\) \(8.496\) \(\Q\) None \(0\) \(0\) \(2\) \(-24\) \(+\) \(-\) \(q+2q^{5}-24q^{7}-44q^{11}+22q^{13}+\cdots\)
144.4.a.f \(1\) \(8.496\) \(\Q\) None \(0\) \(0\) \(16\) \(12\) \(+\) \(+\) \(q+2^{4}q^{5}+12q^{7}-2^{6}q^{11}+58q^{13}+\cdots\)
144.4.a.g \(1\) \(8.496\) \(\Q\) None \(0\) \(0\) \(18\) \(-8\) \(-\) \(-\) \(q+18q^{5}-8q^{7}+6^{2}q^{11}-10q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(144))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(144)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)