Properties

Label 10.5.c
Level $10$
Weight $5$
Character orbit 10.c
Rep. character $\chi_{10}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $7$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 10.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(7\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(10, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4 q + 20 q^{3} - 60 q^{5} - 64 q^{6} + 20 q^{7} + 160 q^{10} + 168 q^{11} + 160 q^{12} - 60 q^{13} + 20 q^{15} - 256 q^{16} - 1020 q^{17} - 640 q^{18} + 968 q^{21} + 1280 q^{22} + 1620 q^{23} - 700 q^{25}+ \cdots + 3840 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.5.c.a 10.c 5.c $2$ $1.034$ \(\Q(\sqrt{-1}) \) None 10.5.c.a \(-4\) \(18\) \(-30\) \(58\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2 i-2)q^{2}+(-9 i+9)q^{3}+\cdots\)
10.5.c.b 10.c 5.c $2$ $1.034$ \(\Q(\sqrt{-1}) \) None 10.5.c.b \(4\) \(2\) \(-30\) \(-38\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2 i+2)q^{2}+(-i+1)q^{3}+8 i q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(10, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)