Properties

Label 576.2.bb
Level $576$
Weight $2$
Character orbit 576.bb
Rep. character $\chi_{576}(49,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $88$
Newform subspaces $5$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(576, [\chi])\).

Total New Old
Modular forms 416 104 312
Cusp forms 352 88 264
Eisenstein series 64 16 48

Trace form

\( 88q + 4q^{3} - 2q^{5} + O(q^{10}) \) \( 88q + 4q^{3} - 2q^{5} + 2q^{11} - 2q^{13} + 8q^{15} - 16q^{17} + 8q^{19} - 10q^{21} - 8q^{27} - 2q^{29} + 4q^{31} - 8q^{33} + 28q^{35} - 8q^{37} + 2q^{43} - 14q^{45} + 44q^{47} + 16q^{49} + 36q^{51} - 8q^{53} - 10q^{59} - 2q^{61} + 36q^{63} - 4q^{65} + 2q^{67} - 10q^{69} - 56q^{75} - 30q^{77} + 4q^{79} - 8q^{81} + 22q^{83} - 12q^{85} + 36q^{91} - 22q^{93} - 60q^{95} - 4q^{97} - 10q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
576.2.bb.a \(4\) \(4.599\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(-12\) \(q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1-\zeta_{12}+\cdots)q^{5}+\cdots\)
576.2.bb.b \(4\) \(4.599\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(12\) \(q+(1-2\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\cdots\)
576.2.bb.c \(4\) \(4.599\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(-6\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
576.2.bb.d \(4\) \(4.599\) \(\Q(\zeta_{12})\) None \(0\) \(6\) \(-8\) \(6\) \(q+(2-\zeta_{12}^{2})q^{3}+(-2-2\zeta_{12}+2\zeta_{12}^{3})q^{5}+\cdots\)
576.2.bb.e \(72\) \(4.599\) None \(0\) \(-2\) \(4\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)