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Properties

Label 1078.4.a
Level $1078$
Weight $4$
Character orbit 1078.a
Rep. character $\chi_{1078}(1,\cdot)$
Character field $\Q$
Dimension $103$
Newform subspaces $30$
Sturm bound $672$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1078.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 30 \)
Sturm bound: \(672\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1078))\).

Total New Old
Modular forms 520 103 417
Cusp forms 488 103 385
Eisenstein series 32 0 32

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

\(2\)\(7\)\(11\)FrickeDim
\(+\)\(+\)\(+\)$+$\(13\)
\(+\)\(+\)\(-\)$-$\(13\)
\(+\)\(-\)\(+\)$-$\(13\)
\(+\)\(-\)\(-\)$+$\(13\)
\(-\)\(+\)\(+\)$-$\(11\)
\(-\)\(+\)\(-\)$+$\(15\)
\(-\)\(-\)\(+\)$+$\(14\)
\(-\)\(-\)\(-\)$-$\(11\)
Plus space\(+\)\(55\)
Minus space\(-\)\(48\)

Trace form

\( 103 q - 2 q^{2} + 10 q^{3} + 412 q^{4} - 28 q^{5} - 8 q^{6} - 8 q^{8} + 941 q^{9} + O(q^{10}) \) \( 103 q - 2 q^{2} + 10 q^{3} + 412 q^{4} - 28 q^{5} - 8 q^{6} - 8 q^{8} + 941 q^{9} + 4 q^{10} + 11 q^{11} + 40 q^{12} + 62 q^{13} - 326 q^{15} + 1648 q^{16} - 66 q^{17} - 106 q^{18} + 92 q^{19} - 112 q^{20} + 22 q^{22} - 158 q^{23} - 32 q^{24} + 2435 q^{25} - 100 q^{26} + 238 q^{27} - 314 q^{29} + 384 q^{30} + 58 q^{31} - 32 q^{32} - 242 q^{33} - 596 q^{34} + 3764 q^{36} + 2012 q^{37} - 320 q^{38} + 2608 q^{39} + 16 q^{40} + 1074 q^{41} + 1192 q^{43} + 44 q^{44} + 1230 q^{45} - 704 q^{46} - 64 q^{47} + 160 q^{48} + 1986 q^{50} + 220 q^{51} + 248 q^{52} + 1130 q^{53} + 1072 q^{54} - 396 q^{55} + 136 q^{57} + 196 q^{58} - 10 q^{59} - 1304 q^{60} - 90 q^{61} + 1328 q^{62} + 6592 q^{64} - 1196 q^{65} - 264 q^{66} - 3006 q^{67} - 264 q^{68} + 98 q^{69} + 2822 q^{71} - 424 q^{72} - 1238 q^{73} - 1052 q^{74} + 1176 q^{75} + 368 q^{76} + 736 q^{78} - 1156 q^{79} - 448 q^{80} + 9039 q^{81} + 1596 q^{82} + 2048 q^{83} - 1312 q^{85} - 104 q^{86} + 3328 q^{87} + 88 q^{88} - 3912 q^{89} + 1156 q^{90} - 632 q^{92} - 5518 q^{93} + 2080 q^{94} + 3040 q^{95} - 128 q^{96} + 844 q^{97} + 77 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1078))\) 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 7 11
1078.4.a.a 1078.a 1.a $1$ $63.604$ \(\Q\) None \(-2\) \(-4\) \(-14\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-4q^{3}+4q^{4}-14q^{5}+8q^{6}+\cdots\)
1078.4.a.b 1078.a 1.a $1$ $63.604$ \(\Q\) None \(-2\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-2q^{5}-8q^{8}-3^{3}q^{9}+\cdots\)
1078.4.a.c 1078.a 1.a $1$ $63.604$ \(\Q\) None \(-2\) \(5\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+5q^{3}+4q^{4}+q^{5}-10q^{6}+\cdots\)
1078.4.a.d 1078.a 1.a $1$ $63.604$ \(\Q\) None \(-2\) \(7\) \(19\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+7q^{3}+4q^{4}+19q^{5}-14q^{6}+\cdots\)
1078.4.a.e 1078.a 1.a $1$ $63.604$ \(\Q\) None \(2\) \(-7\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-7q^{3}+4q^{4}-3q^{5}-14q^{6}+\cdots\)
1078.4.a.f 1078.a 1.a $1$ $63.604$ \(\Q\) None \(2\) \(-1\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+4q^{4}+3q^{5}-2q^{6}+\cdots\)
1078.4.a.g 1078.a 1.a $1$ $63.604$ \(\Q\) None \(2\) \(2\) \(-18\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+4q^{4}-18q^{5}+4q^{6}+\cdots\)
1078.4.a.h 1078.a 1.a $1$ $63.604$ \(\Q\) None \(2\) \(10\) \(14\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+10q^{3}+4q^{4}+14q^{5}+20q^{6}+\cdots\)
1078.4.a.i 1078.a 1.a $2$ $63.604$ \(\Q(\sqrt{37}) \) None \(-4\) \(-6\) \(-26\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-3-\beta )q^{3}+4q^{4}+(-13+\cdots)q^{5}+\cdots\)
1078.4.a.j 1078.a 1.a $2$ $63.604$ \(\Q(\sqrt{137}) \) None \(-4\) \(5\) \(7\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(3-\beta )q^{3}+4q^{4}+(3+\beta )q^{5}+\cdots\)
1078.4.a.k 1078.a 1.a $2$ $63.604$ \(\Q(\sqrt{2}) \) None \(4\) \(-4\) \(24\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2+3\beta )q^{3}+4q^{4}+(12+\cdots)q^{5}+\cdots\)
1078.4.a.l 1078.a 1.a $2$ $63.604$ \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta q^{3}+4q^{4}-3\beta q^{5}+2\beta q^{6}+\cdots\)
1078.4.a.m 1078.a 1.a $2$ $63.604$ \(\Q(\sqrt{2}) \) None \(4\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3\beta q^{3}+4q^{4}+\beta q^{5}+6\beta q^{6}+\cdots\)
1078.4.a.n 1078.a 1.a $2$ $63.604$ \(\Q(\sqrt{2}) \) None \(4\) \(4\) \(-24\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(2+3\beta )q^{3}+4q^{4}+(-12+\cdots)q^{5}+\cdots\)
1078.4.a.o 1078.a 1.a $2$ $63.604$ \(\Q(\sqrt{57}) \) None \(4\) \(5\) \(17\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(3-\beta )q^{3}+4q^{4}+(7+3\beta )q^{5}+\cdots\)
1078.4.a.p 1078.a 1.a $3$ $63.604$ 3.3.7636.1 None \(6\) \(-6\) \(-26\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-9+\cdots)q^{5}+\cdots\)
1078.4.a.q 1078.a 1.a $4$ $63.604$ \(\Q(\sqrt{7}, \sqrt{95})\) None \(-8\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta _{2}q^{3}+4q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
1078.4.a.r 1078.a 1.a $4$ $63.604$ \(\Q(\sqrt{39}, \sqrt{127})\) None \(-8\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta _{1}q^{3}+4q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{6}+\cdots\)
1078.4.a.s 1078.a 1.a $4$ $63.604$ 4.4.112260128.1 None \(8\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
1078.4.a.t 1078.a 1.a $5$ $63.604$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(-7\) \(-20\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
1078.4.a.u 1078.a 1.a $5$ $63.604$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(-1\) \(10\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(2-\beta _{3})q^{5}+\cdots\)
1078.4.a.v 1078.a 1.a $5$ $63.604$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(1\) \(-10\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-2+\beta _{3}+\cdots)q^{5}+\cdots\)
1078.4.a.w 1078.a 1.a $5$ $63.604$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(7\) \(20\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(4+\beta _{3}+\cdots)q^{5}+\cdots\)
1078.4.a.x 1078.a 1.a $5$ $63.604$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-11\) \(-20\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2-\beta _{1})q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
1078.4.a.y 1078.a 1.a $5$ $63.604$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-7\) \(-10\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-1+\beta _{3})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots\)
1078.4.a.z 1078.a 1.a $5$ $63.604$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(7\) \(10\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta _{3})q^{3}+4q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots\)
1078.4.a.ba 1078.a 1.a $5$ $63.604$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(11\) \(20\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(2+\beta _{1})q^{3}+4q^{4}+(4+\beta _{2}+\cdots)q^{5}+\cdots\)
1078.4.a.bb 1078.a 1.a $8$ $63.604$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-\beta _{3}q^{3}+4q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots\)
1078.4.a.bc 1078.a 1.a $8$ $63.604$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta _{5}q^{3}+4q^{4}+(-\beta _{3}+\beta _{6}+\cdots)q^{5}+\cdots\)
1078.4.a.bd 1078.a 1.a $10$ $63.604$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(20\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-\beta _{5}q^{3}+4q^{4}+\beta _{6}q^{5}-2\beta _{5}q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1078))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1078)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 2}\)