↑

Properties

Label 3192.1.m
Level $3192$
Weight $1$
Character orbit 3192.m
Rep. character $\chi_{3192}(797,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $12$
Sturm bound $640$
Trace bound $10$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3192.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3192 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(640\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3192, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 28 28 0
Eisenstein series 8 8 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 28 0 0 0

Trace form

\( 28 q - 4 q^{4} - 8 q^{7} - 8 q^{9} + 12 q^{16} - 4 q^{25} + 4 q^{39} + 6 q^{42} + 16 q^{49} - 4 q^{57} + 8 q^{58} - 6 q^{63} - 4 q^{64} + 16 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(3192, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3192.1.m.a 3192.m 3192.m $1$ $1.593$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) \(\Q(\sqrt{57}) \) 3192.1.m.a \(-1\) \(-1\) \(0\) \(-1\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
3192.1.m.b 3192.m 3192.m $1$ $1.593$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) \(\Q(\sqrt{57}) \) 3192.1.m.a \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
3192.1.m.c 3192.m 3192.m $1$ $1.593$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) \(\Q(\sqrt{57}) \) 3192.1.m.a \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
3192.1.m.d 3192.m 3192.m $1$ $1.593$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-798}) \) \(\Q(\sqrt{57}) \) 3192.1.m.a \(1\) \(1\) \(0\) \(-1\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
3192.1.m.e 3192.m 3192.m $2$ $1.593$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-399}) \) \(\Q(\sqrt{114}) \) 3192.1.m.e \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}-i q^{3}+q^{4}-2 i q^{5}+i q^{6}+\cdots\)
3192.1.m.f 3192.m 3192.m $2$ $1.593$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-38}) \), \(\Q(\sqrt{-399}) \) \(\Q(\sqrt{42}) \) 3192.1.m.f \(0\) \(0\) \(0\) \(2\) \(q-i q^{2}-i q^{3}-q^{4}-q^{6}+q^{7}+\cdots\)
3192.1.m.g 3192.m 3192.m $2$ $1.593$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-38}) \), \(\Q(\sqrt{-399}) \) \(\Q(\sqrt{42}) \) 3192.1.m.f \(0\) \(0\) \(0\) \(2\) \(q+i q^{2}-i q^{3}-q^{4}+q^{6}+q^{7}+\cdots\)
3192.1.m.h 3192.m 3192.m $2$ $1.593$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-14}) \), \(\Q(\sqrt{-399}) \) \(\Q(\sqrt{114}) \) 3192.1.m.e \(2\) \(0\) \(0\) \(2\) \(q+q^{2}-i q^{3}+q^{4}+2 i q^{5}-i q^{6}+\cdots\)
3192.1.m.i 3192.m 3192.m $4$ $1.593$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-38}) \) None 3192.1.m.i \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{4}q^{6}+\cdots\)
3192.1.m.j 3192.m 3192.m $4$ $1.593$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-38}) \) None 3192.1.m.i \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
3192.1.m.k 3192.m 3192.m $4$ $1.593$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-399}) \) None 3192.1.m.k \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)
3192.1.m.l 3192.m 3192.m $4$ $1.593$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-399}) \) None 3192.1.m.k \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{8}^{3}q^{2}+\zeta_{8}^{2}q^{3}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots\)