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Properties

Label 204.4.b
Level $204$
Weight $4$
Character orbit 204.b
Rep. character $\chi_{204}(169,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 204 = 2^{2} \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 204.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(204, [\chi])\).

Total New Old
Modular forms 114 10 104
Cusp forms 102 10 92
Eisenstein series 12 0 12

Trace form

\( 10 q - 90 q^{9} + O(q^{10}) \) \( 10 q - 90 q^{9} + 64 q^{13} + 12 q^{15} - 142 q^{17} - 128 q^{19} + 84 q^{21} - 346 q^{25} + 324 q^{33} + 904 q^{35} + 120 q^{43} - 1216 q^{47} - 2098 q^{49} + 168 q^{51} + 564 q^{53} + 248 q^{55} + 384 q^{59} - 784 q^{67} + 1368 q^{69} + 1272 q^{77} + 810 q^{81} - 3136 q^{83} + 732 q^{85} - 1260 q^{87} + 4516 q^{89} - 12 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(204, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
204.4.b.a 204.b 17.b $10$ $12.036$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(204, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(204, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 3}\)