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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1110))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 37
1110.4.a.a \(1\) \(65.492\) \(\Q\) None \(-2\) \(3\) \(-5\) \(1\) \(+\) \(-\) \(+\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.b \(1\) \(65.492\) \(\Q\) None \(2\) \(-3\) \(-5\) \(10\) \(-\) \(+\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.c \(2\) \(65.492\) \(\Q(\sqrt{33}) \) None \(-4\) \(-6\) \(-10\) \(37\) \(+\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.d \(2\) \(65.492\) \(\Q(\sqrt{61}) \) None \(4\) \(6\) \(10\) \(-30\) \(-\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
1110.4.a.e \(3\) \(65.492\) 3.3.11013.1 None \(-6\) \(-9\) \(-15\) \(2\) \(+\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.f \(3\) \(65.492\) 3.3.243037.1 None \(-6\) \(9\) \(-15\) \(-34\) \(+\) \(-\) \(+\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.g \(3\) \(65.492\) 3.3.837.1 None \(-6\) \(9\) \(15\) \(-12\) \(+\) \(-\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
1110.4.a.h \(3\) \(65.492\) 3.3.1712869.1 None \(6\) \(-9\) \(-15\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.i \(4\) \(65.492\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-12\) \(-20\) \(-35\) \(+\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.j \(4\) \(65.492\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-12\) \(20\) \(9\) \(+\) \(+\) \(-\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
1110.4.a.k \(4\) \(65.492\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(-12\) \(20\) \(-23\) \(-\) \(+\) \(-\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
1110.4.a.l \(4\) \(65.492\) 4.4.8827413.1 None \(8\) \(12\) \(-20\) \(-23\) \(-\) \(-\) \(+\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.m \(5\) \(65.492\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(-15\) \(25\) \(-19\) \(+\) \(+\) \(-\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
1110.4.a.n \(5\) \(65.492\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(15\) \(-25\) \(9\) \(+\) \(-\) \(+\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.o \(5\) \(65.492\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-15\) \(-25\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
1110.4.a.p \(5\) \(65.492\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-15\) \(25\) \(19\) \(-\) \(+\) \(-\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
1110.4.a.q \(5\) \(65.492\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(15\) \(-25\) \(33\) \(-\) \(-\) \(+\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
1110.4.a.r \(6\) \(65.492\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(18\) \(30\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
1110.4.a.s \(7\) \(65.492\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(14\) \(21\) \(35\) \(54\) \(-\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)

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

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