Properties

Label 360.2.s
Level $360$
Weight $2$
Character orbit 360.s
Rep. character $\chi_{360}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 176 12 164
Cusp forms 112 12 100
Eisenstein series 64 0 64

Trace form

\( 12q - 8q^{7} + O(q^{10}) \) \( 12q - 8q^{7} - 4q^{13} + 16q^{25} + 16q^{31} + 28q^{37} - 56q^{55} - 80q^{67} - 52q^{73} + 112q^{91} + 28q^{97} + O(q^{100}) \)

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.s.a \(4\) \(2.875\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(4\zeta_{8}+4\zeta_{8}^{3})q^{11}+\cdots\)
360.2.s.b \(8\) \(2.875\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{7}q^{5}+(-1-\beta _{2}-\beta _{5})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)