Properties

Label 360.2.b
Level $360$
Weight $2$
Character orbit 360.b
Rep. character $\chi_{360}(251,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\), \(23\)

Dimensions

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

Total New Old
Modular forms 80 16 64
Cusp forms 64 16 48
Eisenstein series 16 0 16

Trace form

\( 16q - 4q^{4} + O(q^{10}) \) \( 16q - 4q^{4} + 4q^{10} + 4q^{16} + 16q^{19} - 32q^{22} + 16q^{25} - 16q^{28} - 24q^{34} + 4q^{40} - 16q^{46} + 16q^{49} - 8q^{52} - 40q^{58} - 4q^{64} + 32q^{67} - 24q^{70} + 32q^{73} + 24q^{76} + 88q^{82} - 32q^{88} - 96q^{91} + 88q^{94} - 32q^{97} + O(q^{100}) \)

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.b.a \(2\) \(2.875\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta q^{2}-2q^{4}-q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.b \(2\) \(2.875\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(2\) \(0\) \(q+\beta q^{2}-2q^{4}+q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.c \(6\) \(2.875\) 6.0.2580992.1 None \(-2\) \(0\) \(-6\) \(0\) \(q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
360.2.b.d \(6\) \(2.875\) 6.0.2580992.1 None \(2\) \(0\) \(6\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)