Properties

Label 930.4.a
Level $930$
Weight $4$
Character orbit 930.a
Rep. character $\chi_{930}(1,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $18$
Sturm bound $768$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 930.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(768\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(930))\).

Total New Old
Modular forms 584 60 524
Cusp forms 568 60 508
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.

\(2\)\(3\)\(5\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(36\)
Minus space\(-\)\(24\)

Trace form

\( 60 q + 240 q^{4} + 540 q^{9} + O(q^{10}) \) \( 60 q + 240 q^{4} + 540 q^{9} + 40 q^{10} + 56 q^{11} - 16 q^{14} + 960 q^{16} + 256 q^{17} + 24 q^{19} - 32 q^{23} + 1500 q^{25} - 304 q^{26} - 320 q^{29} + 264 q^{33} + 480 q^{34} - 520 q^{35} + 2160 q^{36} - 368 q^{37} + 160 q^{40} + 936 q^{41} + 96 q^{42} + 544 q^{43} + 224 q^{44} - 784 q^{46} + 640 q^{47} + 4852 q^{49} + 672 q^{51} + 960 q^{53} + 480 q^{55} - 64 q^{56} - 672 q^{58} - 1608 q^{59} + 704 q^{61} + 3840 q^{64} + 360 q^{65} + 1144 q^{67} + 1024 q^{68} - 432 q^{69} + 560 q^{70} + 4864 q^{71} + 1408 q^{73} - 528 q^{74} + 96 q^{76} + 4736 q^{77} + 624 q^{78} + 5024 q^{79} + 4860 q^{81} + 544 q^{82} + 5872 q^{83} + 2592 q^{86} + 912 q^{87} - 2392 q^{89} + 360 q^{90} + 2448 q^{91} - 128 q^{92} + 372 q^{93} + 1824 q^{94} + 2160 q^{95} - 2008 q^{97} + 4096 q^{98} + 504 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(930))\) 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 31
930.4.a.a 930.a 1.a $1$ $54.872$ \(\Q\) None \(-2\) \(-3\) \(5\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
930.4.a.b 930.a 1.a $1$ $54.872$ \(\Q\) None \(2\) \(3\) \(-5\) \(-18\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
930.4.a.c 930.a 1.a $1$ $54.872$ \(\Q\) None \(2\) \(3\) \(-5\) \(26\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
930.4.a.d 930.a 1.a $2$ $54.872$ \(\Q(\sqrt{7}) \) None \(-4\) \(-6\) \(10\) \(18\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
930.4.a.e 930.a 1.a $2$ $54.872$ \(\Q(\sqrt{3}) \) None \(4\) \(6\) \(10\) \(-42\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
930.4.a.f 930.a 1.a $3$ $54.872$ 3.3.54324.2 None \(-6\) \(9\) \(-15\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
930.4.a.g 930.a 1.a $3$ $54.872$ 3.3.4692.1 None \(-6\) \(9\) \(15\) \(-36\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
930.4.a.h 930.a 1.a $3$ $54.872$ 3.3.4692.1 None \(6\) \(-9\) \(-15\) \(-10\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
930.4.a.i 930.a 1.a $3$ $54.872$ 3.3.28024.1 None \(6\) \(-9\) \(15\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
930.4.a.j 930.a 1.a $4$ $54.872$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-12\) \(-20\) \(-7\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
930.4.a.k 930.a 1.a $4$ $54.872$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-12\) \(-20\) \(14\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
930.4.a.l 930.a 1.a $4$ $54.872$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-12\) \(20\) \(-18\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)
930.4.a.m 930.a 1.a $4$ $54.872$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(12\) \(20\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
930.4.a.n 930.a 1.a $4$ $54.872$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(-12\) \(-20\) \(-3\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
930.4.a.o 930.a 1.a $5$ $54.872$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(15\) \(-25\) \(35\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
930.4.a.p 930.a 1.a $5$ $54.872$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-15\) \(25\) \(7\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
930.4.a.q 930.a 1.a $5$ $54.872$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(15\) \(-25\) \(15\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)
930.4.a.r 930.a 1.a $6$ $54.872$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(18\) \(30\) \(21\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(930))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(930)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 2}\)