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Properties

Label 2883.1.o
Level $2883$
Weight $1$
Character orbit 2883.o
Rep. character $\chi_{2883}(338,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $64$
Newform subspaces $5$
Sturm bound $330$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2883 = 3 \cdot 31^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2883.o (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 5 \)
Sturm bound: \(330\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2883, [\chi])\).

Total New Old
Modular forms 320 288 32
Cusp forms 64 64 0
Eisenstein series 256 224 32

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 32 0 32 0

Trace form

\( 64 q - 8 q^{4} - 6 q^{7} + 4 q^{9} + O(q^{10}) \) \( 64 q - 8 q^{4} - 6 q^{7} + 4 q^{9} + 4 q^{10} - 4 q^{18} + 2 q^{19} - 16 q^{25} - 2 q^{28} - 16 q^{36} + 4 q^{39} + 4 q^{40} + 4 q^{45} + 2 q^{49} - 4 q^{51} - 16 q^{63} + 8 q^{67} + 8 q^{70} - 4 q^{72} - 2 q^{76} + 4 q^{82} + 16 q^{87} + 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2883, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2883.1.o.a 2883.o 93.o $8$ $1.439$ \(\Q(\zeta_{15})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None 93.1.l.a \(0\) \(-1\) \(0\) \(-3\) \(q-\zeta_{30}^{2}q^{3}+\zeta_{30}^{6}q^{4}+(\zeta_{30}^{2}-\zeta_{30}^{5}+\cdots)q^{7}+\cdots\)
2883.1.o.b 2883.o 93.o $8$ $1.439$ \(\Q(\zeta_{15})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None 93.1.l.a \(0\) \(-1\) \(0\) \(2\) \(q-\zeta_{30}^{2}q^{3}+\zeta_{30}^{6}q^{4}+(\zeta_{30}^{8}+\zeta_{30}^{14}+\cdots)q^{7}+\cdots\)
2883.1.o.c 2883.o 93.o $8$ $1.439$ \(\Q(\zeta_{15})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None 93.1.l.a \(0\) \(1\) \(0\) \(-3\) \(q+\zeta_{30}^{2}q^{3}+\zeta_{30}^{6}q^{4}+(\zeta_{30}^{2}-\zeta_{30}^{5}+\cdots)q^{7}+\cdots\)
2883.1.o.d 2883.o 93.o $8$ $1.439$ \(\Q(\zeta_{15})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None 93.1.l.a \(0\) \(1\) \(0\) \(2\) \(q+\zeta_{30}^{2}q^{3}+\zeta_{30}^{6}q^{4}+(\zeta_{30}^{8}+\zeta_{30}^{14}+\cdots)q^{7}+\cdots\)
2883.1.o.e 2883.o 93.o $32$ $1.439$ \(\Q(\zeta_{120})\) $S_{4}$ None None 2883.1.b.c \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{120}^{42}q^{2}+\zeta_{120}^{43}q^{3}+\zeta_{120}^{50}q^{5}+\cdots\)