Properties

Label 360.2.q
Level $360$
Weight $2$
Character orbit 360.q
Rep. character $\chi_{360}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $5$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(360, [\chi])\).

Total New Old
Modular forms 160 24 136
Cusp forms 128 24 104
Eisenstein series 32 0 32

Trace form

\( 24q - 2q^{3} - 2q^{5} + 4q^{9} + O(q^{10}) \) \( 24q - 2q^{3} - 2q^{5} + 4q^{9} + 2q^{11} + 28q^{17} - 12q^{19} + 20q^{21} - 12q^{25} + 4q^{27} - 6q^{29} + 12q^{31} - 14q^{33} - 24q^{35} - 36q^{39} - 4q^{41} + 18q^{43} - 12q^{45} + 12q^{47} - 6q^{49} + 14q^{51} + 8q^{53} + 18q^{57} + 2q^{59} + 6q^{61} + 8q^{63} - 8q^{65} + 6q^{67} - 58q^{69} - 8q^{71} + 36q^{73} - 2q^{75} - 40q^{77} + 4q^{81} + 32q^{83} + 8q^{87} - 36q^{89} - 24q^{91} + 8q^{93} - 18q^{97} - 80q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
360.2.q.a \(2\) \(2.875\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(1\) \(0\) \(q+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+\cdots\)
360.2.q.b \(4\) \(2.875\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(-4\) \(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(-2+2\zeta_{12}+\cdots)q^{7}+\cdots\)
360.2.q.c \(4\) \(2.875\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(2\) \(2\) \(-2\) \(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
360.2.q.d \(6\) \(2.875\) 6.0.954288.1 None \(0\) \(-1\) \(-3\) \(5\) \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
360.2.q.e \(8\) \(2.875\) 8.0.856615824.2 None \(0\) \(0\) \(-4\) \(1\) \(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)