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Properties

Label 1150.4.a
Level $1150$
Weight $4$
Character orbit 1150.a
Rep. character $\chi_{1150}(1,\cdot)$
Character field $\Q$
Dimension $104$
Newform subspaces $28$
Sturm bound $720$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1150.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(720\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1150))\).

Total New Old
Modular forms 552 104 448
Cusp forms 528 104 424
Eisenstein series 24 0 24

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

\(2\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(12\)
\(+\)\(+\)\(-\)$-$\(11\)
\(+\)\(-\)\(+\)$-$\(13\)
\(+\)\(-\)\(-\)$+$\(15\)
\(-\)\(+\)\(+\)$-$\(13\)
\(-\)\(+\)\(-\)$+$\(14\)
\(-\)\(-\)\(+\)$+$\(14\)
\(-\)\(-\)\(-\)$-$\(12\)
Plus space\(+\)\(55\)
Minus space\(-\)\(49\)

Trace form

\( 104 q + 4 q^{2} - 8 q^{3} + 416 q^{4} - 32 q^{6} - 16 q^{7} + 16 q^{8} + 864 q^{9} + O(q^{10}) \) \( 104 q + 4 q^{2} - 8 q^{3} + 416 q^{4} - 32 q^{6} - 16 q^{7} + 16 q^{8} + 864 q^{9} - 66 q^{11} - 32 q^{12} - 36 q^{13} + 40 q^{14} + 1664 q^{16} - 96 q^{17} + 52 q^{18} + 182 q^{19} + 380 q^{21} + 148 q^{22} - 128 q^{24} + 248 q^{26} - 428 q^{27} - 64 q^{28} + 256 q^{29} + 76 q^{31} + 64 q^{32} - 716 q^{33} + 120 q^{34} + 3456 q^{36} - 494 q^{37} - 484 q^{38} - 396 q^{39} - 604 q^{41} + 64 q^{42} - 366 q^{43} - 264 q^{44} - 92 q^{46} - 452 q^{47} - 128 q^{48} + 3344 q^{49} + 1808 q^{51} - 144 q^{52} + 182 q^{53} + 568 q^{54} + 160 q^{56} - 256 q^{57} - 64 q^{58} + 384 q^{59} - 3098 q^{61} + 1136 q^{62} + 748 q^{63} + 6656 q^{64} + 1016 q^{66} - 2006 q^{67} - 384 q^{68} - 276 q^{69} + 2028 q^{71} + 208 q^{72} + 1040 q^{73} - 1460 q^{74} + 728 q^{76} + 1496 q^{77} + 2800 q^{78} - 1308 q^{79} + 9176 q^{81} - 656 q^{82} + 1090 q^{83} + 1520 q^{84} - 980 q^{86} + 6212 q^{87} + 592 q^{88} + 44 q^{89} - 2124 q^{91} + 1828 q^{93} - 1328 q^{94} - 512 q^{96} + 464 q^{97} - 28 q^{98} - 3746 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1150))\) 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 23
1150.4.a.a 1150.a 1.a $1$ $67.852$ \(\Q\) None \(-2\) \(-2\) \(0\) \(-21\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-21q^{7}+\cdots\)
1150.4.a.b 1150.a 1.a $1$ $67.852$ \(\Q\) None \(-2\) \(-1\) \(0\) \(18\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+4q^{4}+2q^{6}+18q^{7}+\cdots\)
1150.4.a.c 1150.a 1.a $1$ $67.852$ \(\Q\) None \(-2\) \(1\) \(0\) \(32\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+4q^{4}-2q^{6}+2^{5}q^{7}+\cdots\)
1150.4.a.d 1150.a 1.a $1$ $67.852$ \(\Q\) None \(-2\) \(9\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+9q^{3}+4q^{4}-18q^{6}-2q^{7}+\cdots\)
1150.4.a.e 1150.a 1.a $1$ $67.852$ \(\Q\) None \(2\) \(-7\) \(0\) \(-20\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-7q^{3}+4q^{4}-14q^{6}-20q^{7}+\cdots\)
1150.4.a.f 1150.a 1.a $1$ $67.852$ \(\Q\) None \(2\) \(-4\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-4q^{3}+4q^{4}-8q^{6}-3q^{7}+\cdots\)
1150.4.a.g 1150.a 1.a $1$ $67.852$ \(\Q\) None \(2\) \(1\) \(0\) \(12\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+4q^{4}+2q^{6}+12q^{7}+\cdots\)
1150.4.a.h 1150.a 1.a $1$ $67.852$ \(\Q\) None \(2\) \(2\) \(0\) \(21\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+21q^{7}+\cdots\)
1150.4.a.i 1150.a 1.a $1$ $67.852$ \(\Q\) None \(2\) \(5\) \(0\) \(-12\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+5q^{3}+4q^{4}+10q^{6}-12q^{7}+\cdots\)
1150.4.a.j 1150.a 1.a $2$ $67.852$ \(\Q(\sqrt{73}) \) None \(-4\) \(-3\) \(0\) \(-12\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1-\beta )q^{3}+4q^{4}+(2+2\beta )q^{6}+\cdots\)
1150.4.a.k 1150.a 1.a $2$ $67.852$ \(\Q(\sqrt{41}) \) None \(4\) \(1\) \(0\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-1+3\beta )q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.4.a.l 1150.a 1.a $2$ $67.852$ \(\Q(\sqrt{73}) \) None \(4\) \(3\) \(0\) \(17\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1+\beta )q^{3}+4q^{4}+(2+2\beta )q^{6}+\cdots\)
1150.4.a.m 1150.a 1.a $3$ $67.852$ 3.3.318165.1 None \(6\) \(1\) \(0\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
1150.4.a.n 1150.a 1.a $4$ $67.852$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-14\) \(0\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-4+\beta _{1})q^{3}+4q^{4}+(8-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.o 1150.a 1.a $4$ $67.852$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-4\) \(0\) \(-26\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.p 1150.a 1.a $4$ $67.852$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(4\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.q 1150.a 1.a $5$ $67.852$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(-5\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.r 1150.a 1.a $5$ $67.852$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(0\) \(0\) \(-20\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-4+\cdots)q^{7}+\cdots\)
1150.4.a.s 1150.a 1.a $5$ $67.852$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(12\) \(0\) \(-24\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(2+\beta _{2})q^{3}+4q^{4}+(-4-2\beta _{2}+\cdots)q^{6}+\cdots\)
1150.4.a.t 1150.a 1.a $5$ $67.852$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-12\) \(0\) \(24\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2-\beta _{2})q^{3}+4q^{4}+(-4+\cdots)q^{6}+\cdots\)
1150.4.a.u 1150.a 1.a $5$ $67.852$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(0\) \(0\) \(20\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(4+\cdots)q^{7}+\cdots\)
1150.4.a.v 1150.a 1.a $5$ $67.852$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(5\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.w 1150.a 1.a $6$ $67.852$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(5\) \(0\) \(42\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-2+2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.x 1150.a 1.a $6$ $67.852$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(-5\) \(0\) \(-42\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.4.a.y 1150.a 1.a $7$ $67.852$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-14\) \(9\) \(0\) \(44\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(-2-2\beta _{1}+\cdots)q^{6}+\cdots\)
1150.4.a.z 1150.a 1.a $7$ $67.852$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(14\) \(-9\) \(0\) \(-44\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.4.a.ba 1150.a 1.a $9$ $67.852$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-18\) \(-3\) \(0\) \(-44\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-5+\cdots)q^{7}+\cdots\)
1150.4.a.bb 1150.a 1.a $9$ $67.852$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(18\) \(3\) \(0\) \(44\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(5+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1150))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1150)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 2}\)