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Properties

Label 203.5.c
Level $203$
Weight $5$
Character orbit 203.c
Rep. character $\chi_{203}(202,\cdot)$
Character field $\Q$
Dimension $78$
Newform subspaces $5$
Sturm bound $100$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 203 = 7 \cdot 29 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 203.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 203 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(100\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(203, [\chi])\).

Total New Old
Modular forms 82 82 0
Cusp forms 78 78 0
Eisenstein series 4 4 0

Trace form

\( 78 q - 606 q^{4} - 82 q^{7} + 2126 q^{9} + O(q^{10}) \) \( 78 q - 606 q^{4} - 82 q^{7} + 2126 q^{9} + 4882 q^{16} + 1956 q^{22} - 940 q^{23} - 7038 q^{25} + 4658 q^{28} - 14 q^{29} + 10332 q^{30} + 84 q^{35} - 18878 q^{36} + 3160 q^{42} - 2050 q^{49} - 5028 q^{51} - 3364 q^{53} + 7772 q^{57} - 12068 q^{58} - 8738 q^{63} - 6382 q^{64} + 17484 q^{65} - 8348 q^{67} - 16408 q^{71} + 9528 q^{74} + 11140 q^{78} + 70226 q^{81} - 33276 q^{86} - 47948 q^{88} - 408 q^{91} + 62348 q^{92} - 23416 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(203, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
203.5.c.a 203.c 203.c $1$ $20.984$ \(\Q\) \(\Q(\sqrt{-203}) \) 203.5.c.a \(0\) \(-11\) \(0\) \(49\) $\mathrm{U}(1)[D_{2}]$ \(q-11q^{3}+2^{4}q^{4}+7^{2}q^{7}+40q^{9}+\cdots\)
203.5.c.b 203.c 203.c $1$ $20.984$ \(\Q\) \(\Q(\sqrt{-203}) \) 203.5.c.a \(0\) \(11\) \(0\) \(49\) $\mathrm{U}(1)[D_{2}]$ \(q+11q^{3}+2^{4}q^{4}+7^{2}q^{7}+40q^{9}+\cdots\)
203.5.c.c 203.c 203.c $2$ $20.984$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) 203.5.c.c \(0\) \(0\) \(0\) \(-98\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{2}-47q^{4}-7^{2}q^{7}+31\beta q^{8}+\cdots\)
203.5.c.d 203.c 203.c $2$ $20.984$ \(\Q(\sqrt{203}) \) \(\Q(\sqrt{-203}) \) 203.5.c.d \(0\) \(0\) \(0\) \(-98\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+2^{4}q^{4}-7^{2}q^{7}+122q^{9}+\cdots\)
203.5.c.e 203.c 203.c $72$ $20.984$ None 203.5.c.e \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$