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Properties

Label 111.2.c
Level $111$
Weight $2$
Character orbit 111.c
Rep. character $\chi_{111}(73,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $25$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 111 = 3 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 111.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(25\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(111, [\chi])\).

Total New Old
Modular forms 14 6 8
Cusp forms 10 6 4
Eisenstein series 4 0 4

Trace form

\( 6 q + 2 q^{3} - 2 q^{4} - 8 q^{7} + 6 q^{9} - 4 q^{10} - 6 q^{12} + 2 q^{16} - 8 q^{21} - 2 q^{25} + 2 q^{27} + 8 q^{28} + 4 q^{30} + 4 q^{34} - 2 q^{36} + 2 q^{37} + 36 q^{38} + 12 q^{40} - 12 q^{41} - 48 q^{44}+ \cdots + 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(111, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
111.2.c.a 111.c 37.b $2$ $0.886$ \(\Q(\sqrt{-1}) \) None 111.2.c.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-q^{3}+q^{4}+2 i q^{5}-i q^{6}+\cdots\)
111.2.c.b 111.c 37.b $4$ $0.886$ 4.0.27648.1 None 111.2.c.b \(0\) \(4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(111, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(111, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)