Properties

Label 200.4.c
Level $200$
Weight $4$
Character orbit 200.c
Rep. character $\chi_{200}(49,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $7$
Sturm bound $120$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 200.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(120\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(200, [\chi])\).

Total New Old
Modular forms 102 14 88
Cusp forms 78 14 64
Eisenstein series 24 0 24

Trace form

\( 14 q - 172 q^{9} + O(q^{10}) \) \( 14 q - 172 q^{9} - 94 q^{11} + 46 q^{19} + 460 q^{21} - 368 q^{29} - 492 q^{31} - 40 q^{39} + 1246 q^{41} - 1254 q^{49} - 1230 q^{51} + 704 q^{59} + 572 q^{61} + 700 q^{69} - 2520 q^{71} + 500 q^{79} + 3646 q^{81} + 966 q^{89} - 2368 q^{91} + 7412 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(200, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
200.4.c.a 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5iq^{3}+9iq^{7}-73q^{9}-2^{4}q^{11}+\cdots\)
200.4.c.b 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+9iq^{3}-26iq^{7}-54q^{9}-59q^{11}+\cdots\)
200.4.c.c 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-17iq^{7}-9q^{9}+2^{4}q^{11}+\cdots\)
200.4.c.d 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5iq^{3}-2iq^{7}+2q^{9}+39q^{11}+\cdots\)
200.4.c.e 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+12iq^{7}+11q^{9}-44q^{11}+\cdots\)
200.4.c.f 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-8iq^{7}+11q^{9}+6^{2}q^{11}+\cdots\)
200.4.c.g 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+6iq^{7}+26q^{9}-19q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(200, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)