Properties

Label 7056.2.a
Level $7056$
Weight $2$
Character orbit 7056.a
Rep. character $\chi_{7056}(1,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $77$
Sturm bound $2688$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7056.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 77 \)
Sturm bound: \(2688\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7056))\).

Total New Old
Modular forms 1440 105 1335
Cusp forms 1249 100 1149
Eisenstein series 191 5 186

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

\(2\)\(3\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(12\)
\(-\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(45\)
Minus space\(-\)\(55\)

Trace form

\( 100 q + O(q^{10}) \) \( 100 q + 2 q^{11} + 2 q^{13} - 4 q^{17} - 4 q^{19} + 2 q^{23} + 94 q^{25} + 14 q^{29} - 4 q^{31} + 6 q^{37} - 4 q^{41} - 4 q^{43} - 28 q^{59} + 6 q^{61} - 8 q^{65} - 2 q^{67} - 40 q^{71} + 2 q^{73} - 22 q^{79} + 12 q^{83} + 18 q^{85} - 12 q^{89} - 34 q^{95} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7056))\) 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 7
7056.2.a.a 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-4q^{11}+4q^{13}-4q^{19}+11q^{25}+\cdots\)
7056.2.a.b 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}-3q^{13}+4q^{17}-7q^{19}+4q^{23}+\cdots\)
7056.2.a.c 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-2q^{17}-2q^{19}+8q^{23}+11q^{25}+\cdots\)
7056.2.a.d 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+3q^{13}+4q^{17}+7q^{19}-4q^{23}+\cdots\)
7056.2.a.e 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-3q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\)
7056.2.a.f 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-3q^{11}+2q^{13}-3q^{17}+q^{19}+\cdots\)
7056.2.a.g 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+3q^{11}-4q^{13}+4q^{19}+4q^{25}+\cdots\)
7056.2.a.h 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+3q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\)
7056.2.a.i 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-6q^{11}-3q^{13}-4q^{17}+5q^{19}+\cdots\)
7056.2.a.j 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-6q^{11}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
7056.2.a.k 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{11}-6q^{13}+2q^{17}-4q^{19}+\cdots\)
7056.2.a.l 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{11}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
7056.2.a.m 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{11}-q^{13}+q^{19}-q^{25}+\cdots\)
7056.2.a.n 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{11}-4q^{13}-6q^{17}-8q^{19}+\cdots\)
7056.2.a.o 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{11}+3q^{13}+8q^{17}-q^{19}+\cdots\)
7056.2.a.p 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7056.2.a.q 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
7056.2.a.r 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-5q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\)
7056.2.a.s 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{11}-2q^{13}+3q^{17}+5q^{19}+\cdots\)
7056.2.a.t 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{11}-4q^{13}-4q^{19}+8q^{23}+\cdots\)
7056.2.a.u 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{11}+6q^{13}-5q^{17}+q^{19}+\cdots\)
7056.2.a.v 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+5q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\)
7056.2.a.w 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+5q^{11}+4q^{17}-8q^{19}-4q^{23}+\cdots\)
7056.2.a.x 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-6q^{11}-2q^{13}-4q^{19}-6q^{23}+\cdots\)
7056.2.a.y 7056.a 1.a $1$ $56.342$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $N(\mathrm{U}(1))$ \(q-7q^{13}+7q^{19}-5q^{25}+7q^{31}+\cdots\)
7056.2.a.z 7056.a 1.a $1$ $56.342$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $N(\mathrm{U}(1))$ \(q-5q^{13}-q^{19}-5q^{25}+11q^{31}+\cdots\)
7056.2.a.ba 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{13}+4q^{17}-4q^{19}+4q^{23}+\cdots\)
7056.2.a.bb 7056.a 1.a $1$ $56.342$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{13}+8q^{19}-5q^{25}-4q^{31}+\cdots\)
7056.2.a.bc 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{13}-4q^{17}+4q^{19}+4q^{23}+\cdots\)
7056.2.a.bd 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
7056.2.a.be 7056.a 1.a $1$ $56.342$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $N(\mathrm{U}(1))$ \(q+5q^{13}+q^{19}-5q^{25}-11q^{31}+\cdots\)
7056.2.a.bf 7056.a 1.a $1$ $56.342$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $N(\mathrm{U}(1))$ \(q+7q^{13}-7q^{19}-5q^{25}-7q^{31}+\cdots\)
7056.2.a.bg 7056.a 1.a $1$ $56.342$ \(\Q\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $N(\mathrm{U}(1))$ \(q+4q^{11}+8q^{23}-5q^{25}-2q^{29}+\cdots\)
7056.2.a.bh 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-5q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\)
7056.2.a.bi 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{11}+2q^{13}-3q^{17}-5q^{19}+\cdots\)
7056.2.a.bj 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{11}-6q^{13}+5q^{17}-q^{19}+\cdots\)
7056.2.a.bk 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{11}+4q^{13}+4q^{19}+8q^{23}+\cdots\)
7056.2.a.bl 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+5q^{11}-4q^{17}+8q^{19}-4q^{23}+\cdots\)
7056.2.a.bm 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+5q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\)
7056.2.a.bn 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-6q^{11}+3q^{13}+4q^{17}-5q^{19}+\cdots\)
7056.2.a.bo 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{11}-2q^{13}-6q^{17}+8q^{19}+\cdots\)
7056.2.a.bp 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{11}+q^{13}-q^{19}-q^{25}+\cdots\)
7056.2.a.bq 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-6q^{13}-2q^{17}+4q^{19}-4q^{23}+\cdots\)
7056.2.a.br 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{13}+6q^{17}-4q^{19}-4q^{23}+\cdots\)
7056.2.a.bs 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{11}-3q^{13}-8q^{17}+q^{19}+\cdots\)
7056.2.a.bt 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{11}-2q^{13}+6q^{17}-4q^{19}+\cdots\)
7056.2.a.bu 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{11}+4q^{13}+6q^{17}+8q^{19}+\cdots\)
7056.2.a.bv 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+6q^{11}+6q^{13}-2q^{17}+4q^{19}+\cdots\)
7056.2.a.bw 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-3q^{11}-2q^{13}+3q^{17}-q^{19}+\cdots\)
7056.2.a.bx 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-3q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\)
7056.2.a.by 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}+3q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\)
7056.2.a.bz 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+3q^{11}+4q^{13}-4q^{19}+4q^{25}+\cdots\)
7056.2.a.ca 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-4q^{11}-4q^{13}+4q^{19}+11q^{25}+\cdots\)
7056.2.a.cb 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}-3q^{13}-4q^{17}-7q^{19}-4q^{23}+\cdots\)
7056.2.a.cc 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+3q^{13}-4q^{17}+7q^{19}+4q^{23}+\cdots\)
7056.2.a.cd 7056.a 1.a $1$ $56.342$ \(\Q\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+2q^{11}+6q^{13}-4q^{17}-4q^{19}+\cdots\)
7056.2.a.ce 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}+(-2-2\beta )q^{11}+3\beta q^{13}+\cdots\)
7056.2.a.cf 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}-2q^{11}+(4+\beta )q^{13}+\cdots\)
7056.2.a.cg 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}+(2-2\beta )q^{11}-\beta q^{13}+\cdots\)
7056.2.a.ch 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-\beta q^{11}+(-3+\beta )q^{13}-4q^{17}+\cdots\)
7056.2.a.ci 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-4q^{11}+3\beta q^{13}-5\beta q^{17}+\cdots\)
7056.2.a.cj 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-4q^{11}+\beta q^{13}-2\beta q^{17}+\cdots\)
7056.2.a.ck 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-2q^{11}+2\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cl 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{5}-2q^{11}-\beta q^{17}-5\beta q^{19}+\cdots\)
7056.2.a.cm 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-\beta q^{11}-2q^{13}-\beta q^{17}-4q^{19}+\cdots\)
7056.2.a.cn 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+\beta q^{13}-\beta q^{17}-4q^{23}-3q^{25}+\cdots\)
7056.2.a.co 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{7}) \) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $N(\mathrm{U}(1))$ \(q+\beta q^{11}-\beta q^{23}-5q^{25}-2\beta q^{29}+\cdots\)
7056.2.a.cp 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-\beta q^{13}-\beta q^{17}+4q^{23}-3q^{25}+\cdots\)
7056.2.a.cq 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+2q^{11}-2\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cr 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+4q^{11}-3\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cs 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+4q^{11}-3\beta q^{13}-5\beta q^{17}+\cdots\)
7056.2.a.ct 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{5}+6q^{11}+4\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cu 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-\beta q^{11}+(3-\beta )q^{13}+4q^{17}+\cdots\)
7056.2.a.cv 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}-2q^{11}+(-4+\beta )q^{13}+\cdots\)
7056.2.a.cw 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(-2+2\beta )q^{11}+3\beta q^{13}+\cdots\)
7056.2.a.cx 7056.a 1.a $2$ $56.342$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(2+2\beta )q^{11}-\beta q^{13}+\cdots\)
7056.2.a.cy 7056.a 1.a $4$ $56.342$ \(\Q(\sqrt{2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+\beta _{3}q^{11}-3\beta _{1}q^{13}+\beta _{2}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7056))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7056)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1764))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3528))\)\(^{\oplus 2}\)