Properties

Label 360.2.f
Level $360$
Weight $2$
Character orbit 360.f
Rep. character $\chi_{360}(289,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $144$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 88 8 80
Cusp forms 56 8 48
Eisenstein series 32 0 32

Trace form

\( 8 q - 2 q^{5} + 4 q^{11} + 8 q^{19} + 12 q^{25} + 20 q^{29} + 4 q^{35} - 8 q^{41} - 24 q^{49} - 16 q^{55} - 36 q^{59} - 8 q^{61} - 20 q^{65} - 8 q^{71} + 16 q^{79} + 12 q^{85} + 24 q^{89} - 56 q^{91} + 40 q^{95}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
360.2.f.a 360.f 5.b $2$ $2.875$ \(\Q(\sqrt{-1}) \) None 120.2.f.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(i-2)q^{5}+2 i q^{7}-2 q^{11}+2 i q^{13}+\cdots\)
360.2.f.b 360.f 5.b $2$ $2.875$ \(\Q(\sqrt{-1}) \) None 360.2.f.b \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(i-2)q^{5}-4 i q^{7}+4 q^{11}-4 i q^{13}+\cdots\)
360.2.f.c 360.f 5.b $2$ $2.875$ \(\Q(\sqrt{-1}) \) None 40.2.c.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta+1)q^{5}-\beta q^{7}+4 q^{11}+2\beta q^{13}+\cdots\)
360.2.f.d 360.f 5.b $2$ $2.875$ \(\Q(\sqrt{-1}) \) None 360.2.f.b \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(i+2)q^{5}+4 i q^{7}-4 q^{11}+4 i q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(360, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)