Properties

Label 2240.4.a
Level $2240$
Weight $4$
Character orbit 2240.a
Rep. character $\chi_{2240}(1,\cdot)$
Character field $\Q$
Dimension $144$
Newform subspaces $68$
Sturm bound $1536$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2240.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 68 \)
Sturm bound: \(1536\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2240))\).

Total New Old
Modular forms 1176 144 1032
Cusp forms 1128 144 984
Eisenstein series 48 0 48

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

\(2\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(19\)
\(+\)\(+\)\(-\)\(-\)\(17\)
\(+\)\(-\)\(+\)\(-\)\(16\)
\(+\)\(-\)\(-\)\(+\)\(20\)
\(-\)\(+\)\(+\)\(-\)\(17\)
\(-\)\(+\)\(-\)\(+\)\(19\)
\(-\)\(-\)\(+\)\(+\)\(20\)
\(-\)\(-\)\(-\)\(-\)\(16\)
Plus space\(+\)\(78\)
Minus space\(-\)\(66\)

Trace form

\( 144 q + 1296 q^{9} + O(q^{10}) \) \( 144 q + 1296 q^{9} + 3600 q^{25} - 400 q^{29} - 928 q^{33} - 16 q^{37} - 160 q^{41} + 7056 q^{49} + 752 q^{53} + 1376 q^{57} - 1824 q^{61} - 1056 q^{69} + 1904 q^{77} + 15344 q^{81} + 480 q^{85} - 8544 q^{93} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2240))\) 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 5 7
2240.4.a.a 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-9\) \(-5\) \(-7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-9q^{3}-5q^{5}-7q^{7}+54q^{9}-55q^{11}+\cdots\)
2240.4.a.b 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-8\) \(5\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-8q^{3}+5q^{5}-7q^{7}+37q^{9}+12q^{11}+\cdots\)
2240.4.a.c 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-8\) \(5\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{3}+5q^{5}+7q^{7}+37q^{9}-28q^{11}+\cdots\)
2240.4.a.d 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-8\) \(5\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{3}+5q^{5}+7q^{7}+37q^{9}+68q^{11}+\cdots\)
2240.4.a.e 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-7\) \(-5\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-7q^{3}-5q^{5}+7q^{7}+22q^{9}-9q^{11}+\cdots\)
2240.4.a.f 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-7\) \(5\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-7q^{3}+5q^{5}+7q^{7}+22q^{9}+33q^{11}+\cdots\)
2240.4.a.g 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-5\) \(-5\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-5q^{3}-5q^{5}-7q^{7}-2q^{9}-15q^{11}+\cdots\)
2240.4.a.h 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-5\) \(-5\) \(-7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-5q^{3}-5q^{5}-7q^{7}-2q^{9}+q^{11}+\cdots\)
2240.4.a.i 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-5\) \(5\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{3}+5q^{5}-7q^{7}-2q^{9}+15q^{11}+\cdots\)
2240.4.a.j 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-5\) \(5\) \(-7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{3}+5q^{5}-7q^{7}-2q^{9}+39q^{11}+\cdots\)
2240.4.a.k 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-4\) \(-5\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{3}-5q^{5}-7q^{7}-11q^{9}-6^{2}q^{11}+\cdots\)
2240.4.a.l 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-4\) \(-5\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{3}-5q^{5}-7q^{7}-11q^{9}+20q^{11}+\cdots\)
2240.4.a.m 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-4\) \(-5\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{3}-5q^{5}+7q^{7}-11q^{9}-60q^{11}+\cdots\)
2240.4.a.n 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-4\) \(-5\) \(7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{3}-5q^{5}+7q^{7}-11q^{9}+68q^{11}+\cdots\)
2240.4.a.o 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-4\) \(5\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-4q^{3}+5q^{5}-7q^{7}-11q^{9}+24q^{11}+\cdots\)
2240.4.a.p 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-3\) \(-5\) \(7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}+7q^{7}-18q^{9}-17q^{11}+\cdots\)
2240.4.a.q 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-1\) \(-5\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-5q^{5}-7q^{7}-26q^{9}-39q^{11}+\cdots\)
2240.4.a.r 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-1\) \(5\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+5q^{5}-7q^{7}-26q^{9}-65q^{11}+\cdots\)
2240.4.a.s 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(-1\) \(5\) \(-7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+5q^{5}-7q^{7}-26q^{9}+7q^{11}+\cdots\)
2240.4.a.t 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(1\) \(-5\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-5q^{5}+7q^{7}-26q^{9}+39q^{11}+\cdots\)
2240.4.a.u 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(1\) \(5\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+5q^{5}+7q^{7}-26q^{9}-7q^{11}+\cdots\)
2240.4.a.v 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(1\) \(5\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+5q^{5}+7q^{7}-26q^{9}+65q^{11}+\cdots\)
2240.4.a.w 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(3\) \(-5\) \(-7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-5q^{5}-7q^{7}-18q^{9}+17q^{11}+\cdots\)
2240.4.a.x 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(4\) \(-5\) \(-7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{3}-5q^{5}-7q^{7}-11q^{9}-68q^{11}+\cdots\)
2240.4.a.y 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(4\) \(-5\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{3}-5q^{5}-7q^{7}-11q^{9}+60q^{11}+\cdots\)
2240.4.a.z 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(4\) \(-5\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{3}-5q^{5}+7q^{7}-11q^{9}-20q^{11}+\cdots\)
2240.4.a.ba 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(4\) \(-5\) \(7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{3}-5q^{5}+7q^{7}-11q^{9}+6^{2}q^{11}+\cdots\)
2240.4.a.bb 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(4\) \(5\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{3}+5q^{5}+7q^{7}-11q^{9}-24q^{11}+\cdots\)
2240.4.a.bc 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(5\) \(-5\) \(7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+5q^{3}-5q^{5}+7q^{7}-2q^{9}-q^{11}+\cdots\)
2240.4.a.bd 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(5\) \(-5\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+5q^{3}-5q^{5}+7q^{7}-2q^{9}+15q^{11}+\cdots\)
2240.4.a.be 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(5\) \(5\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{3}+5q^{5}+7q^{7}-2q^{9}-39q^{11}+\cdots\)
2240.4.a.bf 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(5\) \(5\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{3}+5q^{5}+7q^{7}-2q^{9}-15q^{11}+\cdots\)
2240.4.a.bg 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(7\) \(-5\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+7q^{3}-5q^{5}-7q^{7}+22q^{9}+9q^{11}+\cdots\)
2240.4.a.bh 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(7\) \(5\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+7q^{3}+5q^{5}-7q^{7}+22q^{9}-33q^{11}+\cdots\)
2240.4.a.bi 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(8\) \(5\) \(-7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+8q^{3}+5q^{5}-7q^{7}+37q^{9}-68q^{11}+\cdots\)
2240.4.a.bj 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(8\) \(5\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+8q^{3}+5q^{5}-7q^{7}+37q^{9}+28q^{11}+\cdots\)
2240.4.a.bk 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(8\) \(5\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{3}+5q^{5}+7q^{7}+37q^{9}-12q^{11}+\cdots\)
2240.4.a.bl 2240.a 1.a $1$ $132.164$ \(\Q\) None \(0\) \(9\) \(-5\) \(7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+9q^{3}-5q^{5}+7q^{7}+54q^{9}+55q^{11}+\cdots\)
2240.4.a.bm 2240.a 1.a $2$ $132.164$ \(\Q(\sqrt{73}) \) None \(0\) \(-3\) \(10\) \(14\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+5q^{5}+7q^{7}+(-8+\cdots)q^{9}+\cdots\)
2240.4.a.bn 2240.a 1.a $2$ $132.164$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(10\) \(-14\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+5q^{5}-7q^{7}+(6-2\beta )q^{9}+\cdots\)
2240.4.a.bo 2240.a 1.a $2$ $132.164$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(10\) \(14\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+5q^{5}+7q^{7}+(6+2\beta )q^{9}+\cdots\)
2240.4.a.bp 2240.a 1.a $2$ $132.164$ \(\Q(\sqrt{73}) \) None \(0\) \(3\) \(10\) \(-14\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+5q^{5}-7q^{7}+(-8+3\beta )q^{9}+\cdots\)
2240.4.a.bq 2240.a 1.a $3$ $132.164$ 3.3.11853.1 None \(0\) \(-6\) \(-15\) \(21\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}-5q^{5}+7q^{7}+(3-6\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.br 2240.a 1.a $3$ $132.164$ 3.3.11045.1 None \(0\) \(-6\) \(15\) \(-21\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+5q^{5}-7q^{7}+(8-7\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.bs 2240.a 1.a $3$ $132.164$ 3.3.78693.1 None \(0\) \(-2\) \(-15\) \(-21\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-5q^{5}-7q^{7}+(20+\cdots)q^{9}+\cdots\)
2240.4.a.bt 2240.a 1.a $3$ $132.164$ 3.3.14360.1 None \(0\) \(-2\) \(-15\) \(21\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{3}-5q^{5}+7q^{7}+(28+\cdots)q^{9}+\cdots\)
2240.4.a.bu 2240.a 1.a $3$ $132.164$ 3.3.6053.1 None \(0\) \(-2\) \(15\) \(21\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+5q^{5}+7q^{7}+(13+\cdots)q^{9}+\cdots\)
2240.4.a.bv 2240.a 1.a $3$ $132.164$ 3.3.14360.1 None \(0\) \(2\) \(-15\) \(-21\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}-5q^{5}-7q^{7}+(28-3\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.bw 2240.a 1.a $3$ $132.164$ 3.3.78693.1 None \(0\) \(2\) \(-15\) \(21\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-5q^{5}+7q^{7}+(20-2\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.bx 2240.a 1.a $3$ $132.164$ 3.3.6053.1 None \(0\) \(2\) \(15\) \(-21\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+5q^{5}-7q^{7}+(13-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.by 2240.a 1.a $3$ $132.164$ 3.3.11853.1 None \(0\) \(6\) \(-15\) \(-21\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}-5q^{5}-7q^{7}+(3-6\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.bz 2240.a 1.a $3$ $132.164$ 3.3.11045.1 None \(0\) \(6\) \(15\) \(21\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}+5q^{5}+7q^{7}+(8-7\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.ca 2240.a 1.a $4$ $132.164$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-9\) \(-20\) \(-28\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{3}-5q^{5}-7q^{7}+(13+\cdots)q^{9}+\cdots\)
2240.4.a.cb 2240.a 1.a $4$ $132.164$ 4.4.505876.1 None \(0\) \(-7\) \(-20\) \(28\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{3}-5q^{5}+7q^{7}+(12+\cdots)q^{9}+\cdots\)
2240.4.a.cc 2240.a 1.a $4$ $132.164$ 4.4.164244.1 None \(0\) \(-7\) \(20\) \(28\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+5q^{5}+7q^{7}+(11+\cdots)q^{9}+\cdots\)
2240.4.a.cd 2240.a 1.a $4$ $132.164$ 4.4.817716.1 None \(0\) \(-5\) \(-20\) \(-28\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-5q^{5}-7q^{7}+(5-2\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.ce 2240.a 1.a $4$ $132.164$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-3\) \(20\) \(28\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+5q^{5}+7q^{7}+(14+\cdots)q^{9}+\cdots\)
2240.4.a.cf 2240.a 1.a $4$ $132.164$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-1\) \(20\) \(-28\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+5q^{5}-7q^{7}+(5+2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
2240.4.a.cg 2240.a 1.a $4$ $132.164$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(1\) \(20\) \(28\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+5q^{5}+7q^{7}+(5+2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
2240.4.a.ch 2240.a 1.a $4$ $132.164$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(3\) \(20\) \(-28\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+5q^{5}-7q^{7}+(14-\beta _{2}+\cdots)q^{9}+\cdots\)
2240.4.a.ci 2240.a 1.a $4$ $132.164$ 4.4.817716.1 None \(0\) \(5\) \(-20\) \(28\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-5q^{5}+7q^{7}+(5-2\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.cj 2240.a 1.a $4$ $132.164$ 4.4.505876.1 None \(0\) \(7\) \(-20\) \(-28\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta _{2})q^{3}-5q^{5}-7q^{7}+(12+\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.ck 2240.a 1.a $4$ $132.164$ 4.4.164244.1 None \(0\) \(7\) \(20\) \(-28\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}+5q^{5}-7q^{7}+(11+4\beta _{2}+\cdots)q^{9}+\cdots\)
2240.4.a.cl 2240.a 1.a $4$ $132.164$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(9\) \(-20\) \(28\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta _{2})q^{3}-5q^{5}+7q^{7}+(13-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.cm 2240.a 1.a $5$ $132.164$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-11\) \(-25\) \(35\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{3}-5q^{5}+7q^{7}+(13+\cdots)q^{9}+\cdots\)
2240.4.a.cn 2240.a 1.a $5$ $132.164$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-5\) \(25\) \(-35\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+5q^{5}-7q^{7}+(14+\cdots)q^{9}+\cdots\)
2240.4.a.co 2240.a 1.a $5$ $132.164$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(5\) \(25\) \(35\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+5q^{5}+7q^{7}+(14-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.cp 2240.a 1.a $5$ $132.164$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(11\) \(-25\) \(-35\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{3}-5q^{5}-7q^{7}+(13+3\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2240))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2240)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1120))\)\(^{\oplus 2}\)