Properties

Label 2106.2.a
Level $2106$
Weight $2$
Character orbit 2106.a
Rep. character $\chi_{2106}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $22$
Sturm bound $756$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2106.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(756\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2106))\).

Total New Old
Modular forms 402 48 354
Cusp forms 355 48 307
Eisenstein series 47 0 47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(13\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(9\)
Plus space\(+\)\(18\)
Minus space\(-\)\(30\)

Trace form

\( 48 q + 48 q^{4} + 48 q^{16} + 12 q^{19} + 12 q^{22} + 72 q^{25} + 24 q^{31} + 12 q^{34} + 24 q^{37} - 36 q^{43} + 24 q^{46} + 24 q^{49} + 24 q^{58} + 24 q^{61} + 48 q^{64} + 36 q^{67} + 48 q^{70} - 36 q^{73}+ \cdots + 36 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2106))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 13
2106.2.a.a 2106.a 1.a $1$ $16.816$ \(\Q\) None 2106.2.a.a \(-1\) \(0\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
2106.2.a.b 2106.a 1.a $1$ $16.816$ \(\Q\) None 234.2.e.a \(-1\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots\)
2106.2.a.c 2106.a 1.a $1$ $16.816$ \(\Q\) None 2106.2.a.c \(-1\) \(0\) \(2\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
2106.2.a.d 2106.a 1.a $1$ $16.816$ \(\Q\) None 234.2.e.a \(1\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-2q^{7}+q^{8}-2q^{10}+\cdots\)
2106.2.a.e 2106.a 1.a $1$ $16.816$ \(\Q\) None 2106.2.a.c \(1\) \(0\) \(-2\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
2106.2.a.f 2106.a 1.a $1$ $16.816$ \(\Q\) None 2106.2.a.a \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+q^{13}+\cdots\)
2106.2.a.g 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{6}) \) None 2106.2.a.g \(-2\) \(0\) \(-4\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2+\beta )q^{5}+q^{7}-q^{8}+\cdots\)
2106.2.a.h 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{6}) \) None 234.2.e.c \(-2\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}+2q^{7}-q^{8}-\beta q^{10}+\cdots\)
2106.2.a.i 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{3}) \) None 234.2.e.b \(-2\) \(0\) \(2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}-2q^{7}-q^{8}+\cdots\)
2106.2.a.j 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{3}) \) None 2106.2.a.j \(-2\) \(0\) \(2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
2106.2.a.k 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{3}) \) None 2106.2.a.k \(-2\) \(0\) \(2\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}+(1-2\beta )q^{7}+\cdots\)
2106.2.a.l 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{3}) \) None 2106.2.a.j \(2\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+(-2-\beta )q^{7}+\cdots\)
2106.2.a.m 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{3}) \) None 234.2.e.b \(2\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{5}-2q^{7}+q^{8}+\cdots\)
2106.2.a.n 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{3}) \) None 2106.2.a.k \(2\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{5}+(1+2\beta )q^{7}+\cdots\)
2106.2.a.o 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{6}) \) None 234.2.e.c \(2\) \(0\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots\)
2106.2.a.p 2106.a 1.a $2$ $16.816$ \(\Q(\sqrt{6}) \) None 2106.2.a.g \(2\) \(0\) \(4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(2+\beta )q^{5}+q^{7}+q^{8}+\cdots\)
2106.2.a.q 2106.a 1.a $3$ $16.816$ 3.3.321.1 None 234.2.e.d \(-3\) \(0\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2106.2.a.r 2106.a 1.a $3$ $16.816$ 3.3.321.1 None 234.2.e.d \(3\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots\)
2106.2.a.s 2106.a 1.a $4$ $16.816$ \(\Q(\sqrt{3}, \sqrt{7})\) None 2106.2.a.s \(-4\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2106.2.a.t 2106.a 1.a $4$ $16.816$ 4.4.22545.1 None 234.2.e.e \(-4\) \(0\) \(-2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}-q^{8}+\cdots\)
2106.2.a.u 2106.a 1.a $4$ $16.816$ \(\Q(\sqrt{3}, \sqrt{7})\) None 2106.2.a.s \(4\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2106.2.a.v 2106.a 1.a $4$ $16.816$ 4.4.22545.1 None 234.2.e.e \(4\) \(0\) \(2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta _{1}q^{5}+(1+\beta _{3})q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2106))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2106)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(702))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1053))\)\(^{\oplus 2}\)