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Properties

Label 360.6.k
Level $360$
Weight $6$
Character orbit 360.k
Rep. character $\chi_{360}(181,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $4$
Sturm bound $432$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 360.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(432\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(360, [\chi])\).

Total New Old
Modular forms 368 100 268
Cusp forms 352 100 252
Eisenstein series 16 0 16

Trace form

\( 100 q + 2 q^{2} - 12 q^{4} - 196 q^{7} - 604 q^{8} + O(q^{10}) \) \( 100 q + 2 q^{2} - 12 q^{4} - 196 q^{7} - 604 q^{8} + 50 q^{10} + 688 q^{14} + 188 q^{16} - 1900 q^{20} - 548 q^{22} + 8020 q^{23} - 62500 q^{25} + 2064 q^{26} + 11244 q^{28} - 7160 q^{31} + 10612 q^{32} - 23052 q^{34} + 380 q^{38} + 3100 q^{40} - 11608 q^{41} + 700 q^{44} - 52972 q^{46} - 44180 q^{47} + 269364 q^{49} - 1250 q^{50} + 15336 q^{52} - 24200 q^{55} + 150556 q^{56} - 49008 q^{58} + 113480 q^{62} - 117948 q^{64} + 49368 q^{68} + 36400 q^{70} - 200312 q^{71} + 105136 q^{73} - 286888 q^{74} + 336080 q^{76} - 50192 q^{79} - 32400 q^{80} + 40000 q^{82} + 573964 q^{86} - 102256 q^{88} + 3160 q^{89} - 423060 q^{92} - 128188 q^{94} - 144400 q^{95} - 147376 q^{97} - 522234 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
360.6.k.a 360.k 8.b $18$ $57.738$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(0\) \(0\) \(196\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(5-4\beta _{1}-\beta _{11})q^{4}-5^{2}\beta _{1}q^{5}+\cdots\)
360.6.k.b 360.k 8.b $20$ $57.738$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(0\) \(0\) \(-196\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{4}q^{5}+(-10+\cdots)q^{7}+\cdots\)
360.6.k.c 360.k 8.b $22$ $57.738$ None \(2\) \(0\) \(0\) \(196\) $\mathrm{SU}(2)[C_{2}]$
360.6.k.d 360.k 8.b $40$ $57.738$ None \(0\) \(0\) \(0\) \(-392\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)