Properties

Label 360.2.w
Level $360$
Weight $2$
Character orbit 360.w
Rep. character $\chi_{360}(163,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $5$
Sturm bound $144$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(4\)
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 64 96
Cusp forms 128 56 72
Eisenstein series 32 8 24

Trace form

\( 56q + 2q^{2} + 8q^{8} + O(q^{10}) \) \( 56q + 2q^{2} + 8q^{8} + 6q^{10} + 8q^{11} + 20q^{20} - 4q^{22} - 4q^{26} + 12q^{28} + 12q^{32} + 28q^{35} - 36q^{38} + 36q^{40} + 8q^{41} - 36q^{43} - 40q^{46} - 46q^{50} - 4q^{52} - 8q^{56} - 60q^{58} - 24q^{62} + 8q^{65} - 28q^{67} - 68q^{68} - 44q^{70} + 16q^{73} + 24q^{76} - 76q^{80} - 60q^{82} - 36q^{83} + 56q^{86} - 48q^{88} - 40q^{91} - 36q^{92} - 16q^{97} + 94q^{98} + O(q^{100}) \)

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.w.a \(4\) \(2.875\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
360.2.w.b \(4\) \(2.875\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-4\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots\)
360.2.w.c \(8\) \(2.875\) \(\Q(\zeta_{20})\) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{7}q^{2}+\zeta_{20}q^{4}+(1+\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{5}+\cdots\)
360.2.w.d \(16\) \(2.875\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{15}q^{2}-\beta _{2}q^{4}+(\beta _{10}-\beta _{15})q^{5}+\cdots\)
360.2.w.e \(24\) \(2.875\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)