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Properties

Label 6825.2.a
Level $6825$
Weight $2$
Character orbit 6825.a
Rep. character $\chi_{6825}(1,\cdot)$
Character field $\Q$
Dimension $228$
Newform subspaces $57$
Sturm bound $2240$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 6825 = 3 \cdot 5^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6825.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 57 \)
Sturm bound: \(2240\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(2\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6825))\).

Total New Old
Modular forms 1144 228 916
Cusp forms 1097 228 869
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.

\(3\)\(5\)\(7\)\(13\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(13\)
\(+\)\(+\)\(+\)\(-\)$-$\(12\)
\(+\)\(+\)\(-\)\(+\)$-$\(16\)
\(+\)\(+\)\(-\)\(-\)$+$\(13\)
\(+\)\(-\)\(+\)\(+\)$-$\(12\)
\(+\)\(-\)\(+\)\(-\)$+$\(18\)
\(+\)\(-\)\(-\)\(+\)$+$\(14\)
\(+\)\(-\)\(-\)\(-\)$-$\(16\)
\(-\)\(+\)\(+\)\(+\)$-$\(13\)
\(-\)\(+\)\(+\)\(-\)$+$\(10\)
\(-\)\(+\)\(-\)\(+\)$+$\(12\)
\(-\)\(+\)\(-\)\(-\)$-$\(19\)
\(-\)\(-\)\(+\)\(+\)$+$\(16\)
\(-\)\(-\)\(+\)\(-\)$-$\(18\)
\(-\)\(-\)\(-\)\(+\)$-$\(18\)
\(-\)\(-\)\(-\)\(-\)$+$\(8\)
Plus space\(+\)\(104\)
Minus space\(-\)\(124\)

Trace form

\( 228 q + 4 q^{2} + 224 q^{4} - 8 q^{6} + 4 q^{7} + 12 q^{8} + 228 q^{9} + O(q^{10}) \) \( 228 q + 4 q^{2} + 224 q^{4} - 8 q^{6} + 4 q^{7} + 12 q^{8} + 228 q^{9} + 8 q^{11} - 8 q^{12} + 4 q^{14} + 208 q^{16} + 8 q^{17} + 4 q^{18} - 8 q^{19} - 4 q^{21} - 8 q^{22} + 12 q^{23} - 24 q^{24} + 12 q^{28} + 20 q^{29} - 8 q^{31} + 28 q^{32} + 8 q^{33} - 16 q^{34} + 224 q^{36} + 32 q^{37} - 40 q^{38} - 8 q^{39} + 24 q^{41} + 4 q^{43} + 16 q^{44} + 32 q^{46} - 16 q^{47} - 16 q^{48} + 228 q^{49} - 8 q^{51} - 8 q^{52} + 36 q^{53} - 8 q^{54} + 60 q^{56} - 16 q^{57} - 24 q^{58} + 24 q^{59} - 16 q^{61} + 24 q^{62} + 4 q^{63} + 256 q^{64} + 8 q^{66} + 32 q^{67} - 24 q^{69} + 12 q^{72} + 40 q^{73} + 80 q^{74} - 16 q^{76} + 16 q^{77} + 4 q^{78} - 28 q^{79} + 228 q^{81} - 72 q^{82} + 32 q^{83} - 12 q^{84} - 56 q^{86} + 24 q^{87} - 24 q^{88} - 48 q^{89} - 8 q^{91} - 16 q^{92} - 16 q^{93} + 48 q^{94} + 64 q^{96} - 8 q^{97} + 4 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6825))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 7 13
6825.2.a.a 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-2\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
6825.2.a.b 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots\)
6825.2.a.c 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.d 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.e 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.f 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.g 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.h 6825.a 1.a $1$ $54.498$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots\)
6825.2.a.i 6825.a 1.a $1$ $54.498$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
6825.2.a.j 6825.a 1.a $1$ $54.498$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
6825.2.a.k 6825.a 1.a $1$ $54.498$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
6825.2.a.l 6825.a 1.a $1$ $54.498$ \(\Q\) None \(2\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots\)
6825.2.a.m 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
6825.2.a.n 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{13}) \) None \(-1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
6825.2.a.o 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
6825.2.a.p 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
6825.2.a.q 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-\beta q^{6}+q^{7}+\cdots\)
6825.2.a.r 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
6825.2.a.s 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
6825.2.a.t 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{13}) \) None \(1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-\beta q^{6}-q^{7}+\cdots\)
6825.2.a.u 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
6825.2.a.v 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
6825.2.a.w 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(3\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-1-\beta )q^{6}+\cdots\)
6825.2.a.x 6825.a 1.a $3$ $54.498$ 3.3.229.1 None \(0\) \(-3\) \(0\) \(-3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.y 6825.a 1.a $3$ $54.498$ 3.3.621.1 None \(0\) \(-3\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.z 6825.a 1.a $3$ $54.498$ 3.3.837.1 None \(0\) \(-3\) \(0\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.ba 6825.a 1.a $3$ $54.498$ 3.3.229.1 None \(0\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bb 6825.a 1.a $3$ $54.498$ 3.3.229.1 None \(0\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bc 6825.a 1.a $3$ $54.498$ 3.3.621.1 None \(0\) \(3\) \(0\) \(-3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bd 6825.a 1.a $3$ $54.498$ 3.3.316.1 None \(2\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
6825.2.a.be 6825.a 1.a $4$ $54.498$ \(\Q(\zeta_{20})^+\) None \(-2\) \(4\) \(0\) \(4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
6825.2.a.bf 6825.a 1.a $4$ $54.498$ 4.4.14013.1 None \(-1\) \(-4\) \(0\) \(4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bg 6825.a 1.a $4$ $54.498$ 4.4.17428.1 None \(-1\) \(-4\) \(0\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bh 6825.a 1.a $4$ $54.498$ \(\Q(\zeta_{15})^+\) None \(-1\) \(4\) \(0\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots\)
6825.2.a.bi 6825.a 1.a $4$ $54.498$ 4.4.3981.1 None \(-1\) \(4\) \(0\) \(4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bj 6825.a 1.a $4$ $54.498$ 4.4.3981.1 None \(1\) \(-4\) \(0\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bk 6825.a 1.a $4$ $54.498$ \(\Q(\zeta_{15})^+\) None \(1\) \(-4\) \(0\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{2}-\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
6825.2.a.bl 6825.a 1.a $4$ $54.498$ 4.4.14013.1 None \(1\) \(4\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bm 6825.a 1.a $4$ $54.498$ \(\Q(\zeta_{20})^+\) None \(2\) \(-4\) \(0\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{6}+\cdots\)
6825.2.a.bn 6825.a 1.a $4$ $54.498$ 4.4.2225.1 None \(3\) \(-4\) \(0\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6825.2.a.bo 6825.a 1.a $5$ $54.498$ 5.5.255877.1 None \(0\) \(5\) \(0\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(2+\beta _{1})q^{4}-\beta _{2}q^{6}+\cdots\)
6825.2.a.bp 6825.a 1.a $6$ $54.498$ 6.6.259521624.1 None \(-3\) \(6\) \(0\) \(-6\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6825.2.a.bq 6825.a 1.a $6$ $54.498$ 6.6.55102497.1 None \(-2\) \(6\) \(0\) \(6\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.br 6825.a 1.a $6$ $54.498$ 6.6.78539816.1 None \(-1\) \(-6\) \(0\) \(-6\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bs 6825.a 1.a $6$ $54.498$ 6.6.78539816.1 None \(1\) \(6\) \(0\) \(6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bt 6825.a 1.a $6$ $54.498$ 6.6.55102497.1 None \(2\) \(-6\) \(0\) \(-6\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bu 6825.a 1.a $6$ $54.498$ 6.6.259521624.1 None \(3\) \(-6\) \(0\) \(6\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6825.2.a.bv 6825.a 1.a $8$ $54.498$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(-8\) \(0\) \(8\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bw 6825.a 1.a $8$ $54.498$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(8\) \(0\) \(-8\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bx 6825.a 1.a $8$ $54.498$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-8\) \(0\) \(-8\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.by 6825.a 1.a $8$ $54.498$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(8\) \(0\) \(8\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bz 6825.a 1.a $8$ $54.498$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(2\) \(-8\) \(0\) \(8\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.ca 6825.a 1.a $8$ $54.498$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(2\) \(8\) \(0\) \(-8\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.cb 6825.a 1.a $10$ $54.498$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(10\) \(0\) \(-10\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.cc 6825.a 1.a $10$ $54.498$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(-10\) \(0\) \(10\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.cd 6825.a 1.a $12$ $54.498$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-12\) \(0\) \(-12\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.ce 6825.a 1.a $12$ $54.498$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(12\) \(0\) \(12\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6825))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6825)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(975))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1365))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2275))\)\(^{\oplus 2}\)