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Properties

Label 1110.4.a
Level $1110$
Weight $4$
Character orbit 1110.a
Rep. character $\chi_{1110}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $19$
Sturm bound $912$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1110.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(912\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1110))\).

Total New Old
Modular forms 692 72 620
Cusp forms 676 72 604
Eisenstein series 16 0 16

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

\(2\)\(3\)\(5\)\(37\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(3\)
\(+\)\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(+\)\(-\)\(+\)$-$\(4\)
\(+\)\(+\)\(-\)\(-\)$+$\(5\)
\(+\)\(-\)\(+\)\(+\)$-$\(4\)
\(+\)\(-\)\(+\)\(-\)$+$\(5\)
\(+\)\(-\)\(-\)\(+\)$+$\(6\)
\(+\)\(-\)\(-\)\(-\)$-$\(3\)
\(-\)\(+\)\(+\)\(+\)$-$\(5\)
\(-\)\(+\)\(+\)\(-\)$+$\(4\)
\(-\)\(+\)\(-\)\(+\)$+$\(5\)
\(-\)\(+\)\(-\)\(-\)$-$\(4\)
\(-\)\(-\)\(+\)\(+\)$+$\(5\)
\(-\)\(-\)\(+\)\(-\)$-$\(4\)
\(-\)\(-\)\(-\)\(+\)$-$\(2\)
\(-\)\(-\)\(-\)\(-\)$+$\(7\)
Plus space\(+\)\(40\)
Minus space\(-\)\(32\)

Trace form

\( 72 q + 288 q^{4} + 648 q^{9} + O(q^{10}) \) \( 72 q + 288 q^{4} + 648 q^{9} + 160 q^{11} + 168 q^{13} + 160 q^{14} + 1152 q^{16} - 112 q^{17} - 48 q^{22} - 112 q^{23} + 1800 q^{25} + 160 q^{26} - 560 q^{29} - 880 q^{31} + 2592 q^{36} + 148 q^{37} - 1136 q^{38} - 440 q^{41} + 336 q^{42} + 1512 q^{43} + 640 q^{44} + 560 q^{46} + 1472 q^{47} + 3288 q^{49} + 240 q^{51} + 672 q^{52} - 200 q^{53} + 640 q^{56} + 456 q^{57} - 608 q^{58} + 1168 q^{59} + 1632 q^{61} - 2448 q^{62} + 4608 q^{64} + 640 q^{65} + 480 q^{66} - 2448 q^{67} - 448 q^{68} + 960 q^{69} + 912 q^{71} + 3416 q^{73} - 2144 q^{77} - 1056 q^{78} - 592 q^{79} + 5832 q^{81} + 1024 q^{82} - 512 q^{83} - 1360 q^{86} + 96 q^{87} - 192 q^{88} + 1104 q^{89} + 3184 q^{91} - 448 q^{92} - 72 q^{93} - 2240 q^{94} + 2240 q^{95} + 2928 q^{97} + 4096 q^{98} + 1440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1110))\) 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 37
1110.4.a.a 1110.a 1.a $1$ $65.492$ \(\Q\) None \(-2\) \(3\) \(-5\) \(1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.b 1110.a 1.a $1$ $65.492$ \(\Q\) None \(2\) \(-3\) \(-5\) \(10\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.c 1110.a 1.a $2$ $65.492$ \(\Q(\sqrt{33}) \) None \(-4\) \(-6\) \(-10\) \(37\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.d 1110.a 1.a $2$ $65.492$ \(\Q(\sqrt{61}) \) None \(4\) \(6\) \(10\) \(-30\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
1110.4.a.e 1110.a 1.a $3$ $65.492$ 3.3.11013.1 None \(-6\) \(-9\) \(-15\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.f 1110.a 1.a $3$ $65.492$ 3.3.243037.1 None \(-6\) \(9\) \(-15\) \(-34\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.g 1110.a 1.a $3$ $65.492$ 3.3.837.1 None \(-6\) \(9\) \(15\) \(-12\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
1110.4.a.h 1110.a 1.a $3$ $65.492$ 3.3.1712869.1 None \(6\) \(-9\) \(-15\) \(2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.i 1110.a 1.a $4$ $65.492$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-12\) \(-20\) \(-35\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.j 1110.a 1.a $4$ $65.492$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-12\) \(20\) \(9\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
1110.4.a.k 1110.a 1.a $4$ $65.492$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(-12\) \(20\) \(-23\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
1110.4.a.l 1110.a 1.a $4$ $65.492$ 4.4.8827413.1 None \(8\) \(12\) \(-20\) \(-23\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.m 1110.a 1.a $5$ $65.492$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(-15\) \(25\) \(-19\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
1110.4.a.n 1110.a 1.a $5$ $65.492$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(15\) \(-25\) \(9\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.o 1110.a 1.a $5$ $65.492$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-15\) \(-25\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.p 1110.a 1.a $5$ $65.492$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-15\) \(25\) \(19\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
1110.4.a.q 1110.a 1.a $5$ $65.492$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(15\) \(-25\) \(33\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.r 1110.a 1.a $6$ $65.492$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(18\) \(30\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
1110.4.a.s 1110.a 1.a $7$ $65.492$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(14\) \(21\) \(35\) \(54\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1110))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1110)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(555))\)\(^{\oplus 2}\)