Properties

Label 112.6.a
Level $112$
Weight $6$
Character orbit 112.a
Rep. character $\chi_{112}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $11$
Sturm bound $96$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 112.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(112))\).

Total New Old
Modular forms 86 15 71
Cusp forms 74 15 59
Eisenstein series 12 0 12

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

\(2\)\(7\)FrickeDim
\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(7\)
Minus space\(-\)\(8\)

Trace form

\( 15 q + 38 q^{5} - 49 q^{7} + 1259 q^{9} + O(q^{10}) \) \( 15 q + 38 q^{5} - 49 q^{7} + 1259 q^{9} + 1028 q^{11} - 122 q^{13} - 3768 q^{15} + 1206 q^{17} + 2360 q^{19} - 3592 q^{23} + 7817 q^{25} - 576 q^{27} - 2246 q^{29} + 7160 q^{31} - 1920 q^{33} + 7350 q^{35} - 14734 q^{37} + 9144 q^{39} - 7042 q^{41} + 2420 q^{43} + 15390 q^{45} + 34200 q^{47} + 36015 q^{49} - 16368 q^{51} - 32486 q^{53} + 70408 q^{55} - 68648 q^{57} - 29760 q^{59} + 93870 q^{61} - 19845 q^{63} + 55444 q^{65} - 91052 q^{67} - 22320 q^{69} - 138744 q^{71} - 66218 q^{73} + 195488 q^{75} - 3724 q^{77} - 188752 q^{79} + 160415 q^{81} - 122632 q^{83} - 197940 q^{85} - 157072 q^{87} - 248298 q^{89} + 49686 q^{91} + 181968 q^{93} + 14632 q^{95} + 154662 q^{97} + 120628 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(112))\) 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 7
112.6.a.a 112.a 1.a $1$ $17.963$ \(\Q\) None 56.6.a.b \(0\) \(-30\) \(32\) \(-49\) $+$ $+$ $\mathrm{SU}(2)$ \(q-30q^{3}+2^{5}q^{5}-7^{2}q^{7}+657q^{9}+\cdots\)
112.6.a.b 112.a 1.a $1$ $17.963$ \(\Q\) None 28.6.a.b \(0\) \(-26\) \(16\) \(49\) $-$ $-$ $\mathrm{SU}(2)$ \(q-26q^{3}+2^{4}q^{5}+7^{2}q^{7}+433q^{9}+\cdots\)
112.6.a.c 112.a 1.a $1$ $17.963$ \(\Q\) None 14.6.a.a \(0\) \(-10\) \(84\) \(-49\) $-$ $+$ $\mathrm{SU}(2)$ \(q-10q^{3}+84q^{5}-7^{2}q^{7}-143q^{9}+\cdots\)
112.6.a.d 112.a 1.a $1$ $17.963$ \(\Q\) None 14.6.a.b \(0\) \(-8\) \(10\) \(49\) $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{3}+10q^{5}+7^{2}q^{7}-179q^{9}+\cdots\)
112.6.a.e 112.a 1.a $1$ $17.963$ \(\Q\) None 28.6.a.a \(0\) \(2\) \(-96\) \(-49\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-96q^{5}-7^{2}q^{7}-239q^{9}+\cdots\)
112.6.a.f 112.a 1.a $1$ $17.963$ \(\Q\) None 56.6.a.a \(0\) \(6\) \(4\) \(-49\) $+$ $+$ $\mathrm{SU}(2)$ \(q+6q^{3}+4q^{5}-7^{2}q^{7}-207q^{9}+240q^{11}+\cdots\)
112.6.a.g 112.a 1.a $1$ $17.963$ \(\Q\) None 7.6.a.a \(0\) \(14\) \(-56\) \(49\) $-$ $-$ $\mathrm{SU}(2)$ \(q+14q^{3}-56q^{5}+7^{2}q^{7}-47q^{9}+\cdots\)
112.6.a.h 112.a 1.a $2$ $17.963$ \(\Q(\sqrt{57}) \) None 7.6.a.b \(0\) \(6\) \(-18\) \(-98\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(3+3\beta )q^{3}+(-9+5\beta )q^{5}-7^{2}q^{7}+\cdots\)
112.6.a.i 112.a 1.a $2$ $17.963$ \(\Q(\sqrt{345}) \) None 56.6.a.e \(0\) \(6\) \(82\) \(98\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(3+\beta )q^{3}+(41-3\beta )q^{5}+7^{2}q^{7}+\cdots\)
112.6.a.j 112.a 1.a $2$ $17.963$ \(\Q(\sqrt{193}) \) None 56.6.a.d \(0\) \(14\) \(42\) \(98\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(7-\beta )q^{3}+(21-5\beta )q^{5}+7^{2}q^{7}+\cdots\)
112.6.a.k 112.a 1.a $2$ $17.963$ \(\Q(\sqrt{177}) \) None 56.6.a.c \(0\) \(26\) \(-62\) \(-98\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(13-\beta )q^{3}+(-31+5\beta )q^{5}-7^{2}q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(112))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(112)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 2}\)