Properties

Label 6192.2.a
Level $6192$
Weight $2$
Character orbit 6192.a
Rep. character $\chi_{6192}(1,\cdot)$
Character field $\Q$
Dimension $105$
Newform subspaces $55$
Sturm bound $2112$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 6192 = 2^{4} \cdot 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6192.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 55 \)
Sturm bound: \(2112\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6192))\).

Total New Old
Modular forms 1080 105 975
Cusp forms 1033 105 928
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.

\(2\)\(3\)\(43\)FrickeDim
\(+\)\(+\)\(+\)$+$\(8\)
\(+\)\(+\)\(-\)$-$\(14\)
\(+\)\(-\)\(+\)$-$\(17\)
\(+\)\(-\)\(-\)$+$\(14\)
\(-\)\(+\)\(+\)$-$\(10\)
\(-\)\(+\)\(-\)$+$\(10\)
\(-\)\(-\)\(+\)$+$\(16\)
\(-\)\(-\)\(-\)$-$\(16\)
Plus space\(+\)\(48\)
Minus space\(-\)\(57\)

Trace form

\( 105 q - 2 q^{5} + O(q^{10}) \) \( 105 q - 2 q^{5} - 6 q^{11} - 2 q^{13} + 2 q^{17} + 8 q^{19} + 6 q^{23} + 115 q^{25} - 2 q^{29} + 2 q^{31} - 24 q^{35} - 2 q^{37} - 6 q^{41} + 3 q^{43} - 8 q^{47} + 105 q^{49} - 10 q^{53} - 26 q^{61} + 20 q^{65} - 6 q^{67} - 12 q^{71} + 18 q^{73} + 8 q^{77} + 4 q^{79} - 6 q^{83} - 4 q^{85} + 2 q^{89} + 24 q^{91} - 52 q^{95} - 6 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6192))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 43
6192.2.a.a 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-3\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-5q^{7}-3q^{11}-q^{13}+6q^{17}+\cdots\)
6192.2.a.b 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}-q^{11}+q^{13}-4q^{17}+\cdots\)
6192.2.a.c 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}-q^{11}+7q^{13}+2q^{17}+\cdots\)
6192.2.a.d 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-3\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}+3q^{11}-q^{13}-6q^{17}+\cdots\)
6192.2.a.e 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}+2q^{11}+2q^{13}-4q^{17}+\cdots\)
6192.2.a.f 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}-6q^{11}-6q^{13}-8q^{19}+\cdots\)
6192.2.a.g 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{13}+6q^{17}-4q^{19}-4q^{23}+\cdots\)
6192.2.a.h 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
6192.2.a.i 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+q^{11}+q^{13}+4q^{17}+\cdots\)
6192.2.a.j 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}+3q^{11}-5q^{13}+6q^{17}+\cdots\)
6192.2.a.k 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(-1\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+5q^{7}+q^{11}-3q^{13}+7q^{19}+\cdots\)
6192.2.a.l 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{11}+6q^{13}-6q^{17}-4q^{19}+\cdots\)
6192.2.a.m 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{11}-q^{13}+3q^{17}-2q^{19}+\cdots\)
6192.2.a.n 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+5q^{11}-7q^{13}-4q^{17}+\cdots\)
6192.2.a.o 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+3q^{11}-3q^{13}-5q^{19}+\cdots\)
6192.2.a.p 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}-3q^{11}-5q^{13}-6q^{17}+\cdots\)
6192.2.a.q 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}-2q^{11}+2q^{13}+4q^{17}+\cdots\)
6192.2.a.r 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}+4q^{11}+6q^{13}+6q^{17}+\cdots\)
6192.2.a.s 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-3q^{11}-q^{13}+3q^{17}+\cdots\)
6192.2.a.t 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
6192.2.a.u 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}+6q^{11}-6q^{13}-8q^{19}+\cdots\)
6192.2.a.v 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}-5q^{11}+3q^{13}+3q^{17}+\cdots\)
6192.2.a.w 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+q^{11}-q^{13}+7q^{17}+\cdots\)
6192.2.a.x 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}-3q^{11}-q^{13}+6q^{17}+\cdots\)
6192.2.a.y 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(3\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+3q^{7}-5q^{11}-3q^{13}-7q^{19}+\cdots\)
6192.2.a.z 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+3q^{7}+3q^{11}+q^{13}-4q^{17}+\cdots\)
6192.2.a.ba 6192.a 1.a $1$ $49.443$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+3q^{11}-5q^{13}+3q^{17}+2q^{19}+\cdots\)
6192.2.a.bb 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{41}) \) None \(0\) \(0\) \(-4\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}+(3-\beta )q^{11}+(1-\beta )q^{13}+\cdots\)
6192.2.a.bc 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-4\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-2\beta q^{7}+(-4+\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
6192.2.a.bd 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}+(2-\beta )q^{7}+(-1+2\beta )q^{11}+\cdots\)
6192.2.a.be 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{21}) \) None \(0\) \(0\) \(-3\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-2q^{7}+2q^{13}+(4+\beta )q^{17}+\cdots\)
6192.2.a.bf 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(-1-\beta )q^{7}+(3-\beta )q^{11}+\cdots\)
6192.2.a.bg 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(-1+2\beta )q^{7}+(3-\beta )q^{11}+\cdots\)
6192.2.a.bh 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+\beta q^{7}+5q^{11}-q^{13}+(1-\beta )q^{17}+\cdots\)
6192.2.a.bi 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{5}-2q^{7}+3\beta q^{11}+5q^{13}+\cdots\)
6192.2.a.bj 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+\beta q^{7}+(1-2\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
6192.2.a.bk 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+3\beta q^{11}-q^{13}+2\beta q^{17}+\cdots\)
6192.2.a.bl 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+\beta q^{7}+(2+\beta )q^{11}+(-2+\beta )q^{13}+\cdots\)
6192.2.a.bm 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(1-2\beta )q^{7}+(-5+\beta )q^{11}+\cdots\)
6192.2.a.bn 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(1+\beta )q^{7}-3q^{11}-3q^{13}+\cdots\)
6192.2.a.bo 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1-\beta )q^{7}+(-3+\beta )q^{11}+\cdots\)
6192.2.a.bp 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-2+4\beta )q^{7}+(-4+4\beta )q^{11}+\cdots\)
6192.2.a.bq 6192.a 1.a $2$ $49.443$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(3-\beta )q^{7}+q^{11}+(-3+\cdots)q^{13}+\cdots\)
6192.2.a.br 6192.a 1.a $3$ $49.443$ 3.3.568.1 None \(0\) \(0\) \(-4\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+(1+\cdots)q^{11}+\cdots\)
6192.2.a.bs 6192.a 1.a $3$ $49.443$ 3.3.568.1 None \(0\) \(0\) \(-4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+(-3+\cdots)q^{11}+\cdots\)
6192.2.a.bt 6192.a 1.a $3$ $49.443$ 3.3.229.1 None \(0\) \(0\) \(-1\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}-2q^{7}+(3\beta _{1}-\beta _{2})q^{11}+(2+\cdots)q^{13}+\cdots\)
6192.2.a.bu 6192.a 1.a $3$ $49.443$ 3.3.148.1 None \(0\) \(0\) \(-1\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+q^{7}+\beta _{1}q^{11}+(-1+\beta _{1}+\cdots)q^{13}+\cdots\)
6192.2.a.bv 6192.a 1.a $3$ $49.443$ 3.3.148.1 None \(0\) \(0\) \(1\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+q^{7}-\beta _{1}q^{11}+(-1+\beta _{1}+\cdots)q^{13}+\cdots\)
6192.2.a.bw 6192.a 1.a $3$ $49.443$ 3.3.568.1 None \(0\) \(0\) \(4\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
6192.2.a.bx 6192.a 1.a $3$ $49.443$ 3.3.3592.1 None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+(1-\beta _{1})q^{11}+\cdots\)
6192.2.a.by 6192.a 1.a $4$ $49.443$ 4.4.60112.1 None \(0\) \(0\) \(0\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{3})q^{7}-\beta _{2}q^{11}+\cdots\)
6192.2.a.bz 6192.a 1.a $4$ $49.443$ \(\Q(\sqrt{5}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+(1+\beta _{2})q^{7}-\beta _{1}q^{11}+(3+\cdots)q^{13}+\cdots\)
6192.2.a.ca 6192.a 1.a $5$ $49.443$ 5.5.7998268.1 None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{5}+(-1+\beta _{2}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
6192.2.a.cb 6192.a 1.a $6$ $49.443$ 6.6.824018032.1 None \(0\) \(0\) \(-5\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+(1+\beta _{1}+\beta _{4})q^{7}+\cdots\)
6192.2.a.cc 6192.a 1.a $6$ $49.443$ 6.6.824018032.1 None \(0\) \(0\) \(5\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{5}+(1+\beta _{1}+\beta _{4})q^{7}+\beta _{2}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6192))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6192)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(129))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(172))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(258))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(344))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(387))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(516))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(688))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(774))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1032))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1548))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2064))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3096))\)\(^{\oplus 2}\)