Properties

Label 7200.2.a
Level $7200$
Weight $2$
Character orbit 7200.a
Rep. character $\chi_{7200}(1,\cdot)$
Character field $\Q$
Dimension $95$
Newform subspaces $72$
Sturm bound $2880$
Trace bound $23$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7200.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 72 \)
Sturm bound: \(2880\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7200))\).

Total New Old
Modular forms 1536 95 1441
Cusp forms 1345 95 1250
Eisenstein series 191 0 191

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

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(-\)\(+\)\(14\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(10\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(16\)
Plus space\(+\)\(45\)
Minus space\(-\)\(50\)

Trace form

\( 95 q + O(q^{10}) \) \( 95 q - 6 q^{13} - 2 q^{17} - 6 q^{29} - 6 q^{37} - 10 q^{41} + 87 q^{49} + 18 q^{53} - 14 q^{61} - 34 q^{73} - 16 q^{77} + 22 q^{89} - 10 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7200))\) 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 5
7200.2.a.a 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-4q^{13}+8q^{19}-4q^{23}+6q^{29}+\cdots\)
7200.2.a.b 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{7}+2q^{13}-6q^{17}+4q^{23}+2q^{29}+\cdots\)
7200.2.a.c 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}+4q^{13}-8q^{19}-4q^{23}+6q^{29}+\cdots\)
7200.2.a.d 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{7}+4q^{11}-6q^{13}+2q^{17}-4q^{19}+\cdots\)
7200.2.a.e 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{7}+4q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7200.2.a.f 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{7}-4q^{11}-7q^{13}-4q^{17}-q^{19}+\cdots\)
7200.2.a.g 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{7}-5q^{13}+5q^{19}-4q^{23}-4q^{29}+\cdots\)
7200.2.a.h 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{7}+5q^{13}-5q^{19}-4q^{23}-4q^{29}+\cdots\)
7200.2.a.i 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{7}+4q^{11}+7q^{13}+4q^{17}+q^{19}+\cdots\)
7200.2.a.j 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-6q^{11}-2q^{13}+6q^{17}-4q^{19}+\cdots\)
7200.2.a.k 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-5q^{11}-5q^{17}+5q^{19}-6q^{23}+\cdots\)
7200.2.a.l 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-4q^{11}+6q^{13}+2q^{17}-8q^{19}+\cdots\)
7200.2.a.m 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-2q^{11}-2q^{17}+4q^{19}-2q^{29}+\cdots\)
7200.2.a.n 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+2q^{11}+2q^{17}+4q^{19}+2q^{29}+\cdots\)
7200.2.a.o 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+5q^{11}+5q^{17}-5q^{19}-6q^{23}+\cdots\)
7200.2.a.p 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+6q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7200.2.a.q 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}-4q^{11}-3q^{13}+4q^{17}+q^{19}+\cdots\)
7200.2.a.r 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-q^{13}+3q^{19}+4q^{23}-4q^{29}+\cdots\)
7200.2.a.s 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}+q^{13}-3q^{19}+4q^{23}-4q^{29}+\cdots\)
7200.2.a.t 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{11}+3q^{13}-4q^{17}-q^{19}+\cdots\)
7200.2.a.u 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{11}-2q^{13}-2q^{17}+8q^{19}+\cdots\)
7200.2.a.v 7200.a 1.a $1$ $57.492$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $N(\mathrm{U}(1))$ \(q-6q^{13}+2q^{17}+10q^{29}+2q^{37}+\cdots\)
7200.2.a.w 7200.a 1.a $1$ $57.492$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $N(\mathrm{U}(1))$ \(q-4q^{13}-2q^{17}+4q^{29}+12q^{37}+\cdots\)
7200.2.a.x 7200.a 1.a $1$ $57.492$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $N(\mathrm{U}(1))$ \(q-4q^{13}+2q^{17}-4q^{29}+12q^{37}+\cdots\)
7200.2.a.y 7200.a 1.a $1$ $57.492$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $N(\mathrm{U}(1))$ \(q-4q^{13}+8q^{17}-10q^{29}-12q^{37}+\cdots\)
7200.2.a.z 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{13}+6q^{17}-4q^{19}+8q^{23}+\cdots\)
7200.2.a.ba 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{13}+6q^{17}+4q^{19}-8q^{23}+\cdots\)
7200.2.a.bb 7200.a 1.a $1$ $57.492$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $N(\mathrm{U}(1))$ \(q+4q^{13}-8q^{17}-10q^{29}+12q^{37}+\cdots\)
7200.2.a.bc 7200.a 1.a $1$ $57.492$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $N(\mathrm{U}(1))$ \(q+4q^{13}-2q^{17}-4q^{29}-12q^{37}+\cdots\)
7200.2.a.bd 7200.a 1.a $1$ $57.492$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $N(\mathrm{U}(1))$ \(q+4q^{13}+2q^{17}+4q^{29}-12q^{37}+\cdots\)
7200.2.a.be 7200.a 1.a $1$ $57.492$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $N(\mathrm{U}(1))$ \(q+6q^{13}-8q^{17}-4q^{29}+2q^{37}+\cdots\)
7200.2.a.bf 7200.a 1.a $1$ $57.492$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $N(\mathrm{U}(1))$ \(q+6q^{13}+8q^{17}+4q^{29}+2q^{37}+\cdots\)
7200.2.a.bg 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{11}-2q^{13}-2q^{17}-8q^{19}+\cdots\)
7200.2.a.bh 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}+3q^{13}-4q^{17}+q^{19}+\cdots\)
7200.2.a.bi 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-q^{13}-3q^{19}-4q^{23}-4q^{29}+\cdots\)
7200.2.a.bj 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+q^{13}+3q^{19}-4q^{23}-4q^{29}+\cdots\)
7200.2.a.bk 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}-3q^{13}+4q^{17}-q^{19}+\cdots\)
7200.2.a.bl 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-6q^{11}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
7200.2.a.bm 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-5q^{11}+5q^{17}+5q^{19}+6q^{23}+\cdots\)
7200.2.a.bn 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-2q^{11}+2q^{17}-4q^{19}+2q^{29}+\cdots\)
7200.2.a.bo 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}+2q^{11}-2q^{17}-4q^{19}-2q^{29}+\cdots\)
7200.2.a.bp 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}+4q^{11}+6q^{13}+2q^{17}+8q^{19}+\cdots\)
7200.2.a.bq 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+5q^{11}-5q^{17}-5q^{19}+6q^{23}+\cdots\)
7200.2.a.br 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+6q^{11}-2q^{13}+6q^{17}+4q^{19}+\cdots\)
7200.2.a.bs 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{7}-4q^{11}+7q^{13}+4q^{17}-q^{19}+\cdots\)
7200.2.a.bt 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{7}-5q^{13}-5q^{19}+4q^{23}-4q^{29}+\cdots\)
7200.2.a.bu 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{7}+5q^{13}+5q^{19}+4q^{23}-4q^{29}+\cdots\)
7200.2.a.bv 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{7}+4q^{11}-7q^{13}-4q^{17}+q^{19}+\cdots\)
7200.2.a.bw 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-4q^{11}-6q^{13}+2q^{17}+4q^{19}+\cdots\)
7200.2.a.bx 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-4q^{11}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
7200.2.a.by 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-4q^{13}-8q^{19}+4q^{23}+6q^{29}+\cdots\)
7200.2.a.bz 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{7}+2q^{13}-6q^{17}-4q^{23}+2q^{29}+\cdots\)
7200.2.a.ca 7200.a 1.a $1$ $57.492$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}+4q^{13}+8q^{19}+4q^{23}+6q^{29}+\cdots\)
7200.2.a.cb 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(-6\) $+$ $-$ $-$ $N(\mathrm{U}(1))$ \(q+(-3-\beta )q^{7}+(1+3\beta )q^{23}+6q^{29}+\cdots\)
7200.2.a.cc 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-\beta q^{11}-\beta q^{13}-\beta q^{17}+4q^{23}+\cdots\)
7200.2.a.cd 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{7}-2q^{11}-3q^{13}+2\beta q^{17}+\cdots\)
7200.2.a.ce 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{7}-2q^{11}+3q^{13}+2\beta q^{17}+\cdots\)
7200.2.a.cf 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2\beta q^{7}-\beta q^{11}-4q^{13}-7q^{17}+\cdots\)
7200.2.a.cg 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{7}-\beta q^{11}-4q^{13}-2q^{17}-2\beta q^{23}+\cdots\)
7200.2.a.ch 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{7}+\beta q^{11}-4q^{13}+2q^{17}+2\beta q^{23}+\cdots\)
7200.2.a.ci 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{7}+2\beta q^{11}-q^{13}-2q^{17}+3\beta q^{19}+\cdots\)
7200.2.a.cj 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{7}-2\beta q^{11}-q^{13}+2q^{17}+3\beta q^{19}+\cdots\)
7200.2.a.ck 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{7}+2\beta q^{11}+q^{13}-2q^{17}-3\beta q^{19}+\cdots\)
7200.2.a.cl 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{7}-2\beta q^{11}+q^{13}+2q^{17}-3\beta q^{19}+\cdots\)
7200.2.a.cm 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{7}+2\beta q^{11}+2q^{13}+2q^{17}+\cdots\)
7200.2.a.cn 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2\beta q^{7}+\beta q^{11}+4q^{13}+7q^{17}+\cdots\)
7200.2.a.co 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{7}+2q^{11}-3q^{13}-2\beta q^{17}+\cdots\)
7200.2.a.cp 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{7}+2q^{11}+3q^{13}-2\beta q^{17}+\cdots\)
7200.2.a.cq 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+\beta q^{11}-\beta q^{13}-\beta q^{17}-4q^{23}+\cdots\)
7200.2.a.cr 7200.a 1.a $2$ $57.492$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(6\) $-$ $-$ $-$ $N(\mathrm{U}(1))$ \(q+(3+\beta )q^{7}+(-1-3\beta )q^{23}+6q^{29}+\cdots\)
7200.2.a.cs 7200.a 1.a $4$ $57.492$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{7}-\beta _{2}q^{11}+\beta _{2}q^{13}+\beta _{3}q^{17}+\cdots\)
7200.2.a.ct 7200.a 1.a $4$ $57.492$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{7}+\beta _{2}q^{11}+\beta _{2}q^{13}-\beta _{3}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(900))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1800))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3600))\)\(^{\oplus 2}\)