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Properties

Label 200.2.m
Level $200$
Weight $2$
Character orbit 200.m
Rep. character $\chi_{200}(41,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $28$
Newform subspaces $3$
Sturm bound $60$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 200.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(200, [\chi])\).

Total New Old
Modular forms 136 28 108
Cusp forms 104 28 76
Eisenstein series 32 0 32

Trace form

\( 28 q - q^{5} + 4 q^{7} - 5 q^{9} + O(q^{10}) \) \( 28 q - q^{5} + 4 q^{7} - 5 q^{9} - 6 q^{11} + 2 q^{13} - 20 q^{15} - 2 q^{17} - 6 q^{19} + 4 q^{21} + 26 q^{23} - q^{25} + 8 q^{29} - 6 q^{31} + 4 q^{35} + 29 q^{37} - 12 q^{39} + 10 q^{41} - 32 q^{43} - 67 q^{45} - 24 q^{47} + 60 q^{51} - 21 q^{53} - 24 q^{55} - 80 q^{57} - 30 q^{59} - 4 q^{61} - 32 q^{63} + 7 q^{65} - 8 q^{67} - 4 q^{69} - 12 q^{71} - 34 q^{73} + 16 q^{77} + 16 q^{79} + 37 q^{81} + 46 q^{83} + 13 q^{85} + 10 q^{87} + 9 q^{89} + 4 q^{91} + 120 q^{93} + 56 q^{95} + 44 q^{97} + 92 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(200, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
200.2.m.a 200.m 25.d $4$ $1.597$ \(\Q(\zeta_{10})\) None 200.2.m.a \(0\) \(5\) \(-5\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-2\zeta_{10}-\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots\)
200.2.m.b 200.m 25.d $8$ $1.597$ 8.0.58140625.2 None 200.2.m.b \(0\) \(-6\) \(5\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\beta _{2})q^{3}+(1+\beta _{5})q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
200.2.m.c 200.m 25.d $16$ $1.597$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 200.2.m.c \(0\) \(1\) \(-1\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{4}+\beta _{5}+\beta _{14}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

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