Properties

Label 600.2.m
Level $600$
Weight $2$
Character orbit 600.m
Rep. character $\chi_{600}(299,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $5$
Sturm bound $240$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 120 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(240\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(7\), \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(600, [\chi])\).

Total New Old
Modular forms 132 76 56
Cusp forms 108 68 40
Eisenstein series 24 8 16

Trace form

\( 68 q + 2 q^{6} + 4 q^{9} + O(q^{10}) \) \( 68 q + 2 q^{6} + 4 q^{9} + 8 q^{16} + 24 q^{19} - 6 q^{24} + 4 q^{34} + 26 q^{36} - 64 q^{46} + 52 q^{49} + 8 q^{51} - 16 q^{54} - 24 q^{64} - 66 q^{66} - 124 q^{76} + 12 q^{81} - 44 q^{84} + 48 q^{91} + 104 q^{94} - 114 q^{96} - 96 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
600.2.m.a 600.m 120.m $4$ $4.791$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+2q^{4}+\cdots\)
600.2.m.b 600.m 120.m $8$ $4.791$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{3}q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots\)
600.2.m.c 600.m 120.m $16$ $4.791$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-1+\beta _{11}+\cdots)q^{6}+\cdots\)
600.2.m.d 600.m 120.m $16$ $4.791$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}-\beta _{14}q^{6}+\cdots\)
600.2.m.e 600.m 120.m $24$ $4.791$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)