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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
200.4.c.a 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None 40.4.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5\beta q^{3}+9\beta q^{7}-73 q^{9}-16 q^{11}+\cdots\)
200.4.c.b 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None 200.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+9 i q^{3}-26 i q^{7}-54 q^{9}-59 q^{11}+\cdots\)
200.4.c.c 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None 40.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\beta q^{3}-17\beta q^{7}-9 q^{9}+16 q^{11}+\cdots\)
200.4.c.d 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None 200.4.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5 i q^{3}-2 i q^{7}+2 q^{9}+39 q^{11}+\cdots\)
200.4.c.e 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None 8.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{3}+12\beta q^{7}+11 q^{9}-44 q^{11}+\cdots\)
200.4.c.f 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None 40.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{3}-8\beta q^{7}+11 q^{9}+36 q^{11}+\cdots\)
200.4.c.g 200.c 5.b $2$ $11.800$ \(\Q(\sqrt{-1}) \) None 200.4.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{3}+6 i q^{7}+26 q^{9}-19 q^{11}+\cdots\)

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

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