Properties

Label 1075.6.a
Level $1075$
Weight $6$
Character orbit 1075.a
Rep. character $\chi_{1075}(1,\cdot)$
Character field $\Q$
Dimension $332$
Newform subspaces $12$
Sturm bound $660$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(660\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(1075))\).

Total New Old
Modular forms 556 332 224
Cusp forms 544 332 212
Eisenstein series 12 0 12

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

\(5\)\(43\)FrickeDim.
\(+\)\(+\)\(+\)\(76\)
\(+\)\(-\)\(-\)\(82\)
\(-\)\(+\)\(-\)\(89\)
\(-\)\(-\)\(+\)\(85\)
Plus space\(+\)\(161\)
Minus space\(-\)\(171\)

Trace form

\( 332 q + 4 q^{2} - 2 q^{3} + 5276 q^{4} + 222 q^{6} + 76 q^{7} - 480 q^{8} + 26448 q^{9} + O(q^{10}) \) \( 332 q + 4 q^{2} - 2 q^{3} + 5276 q^{4} + 222 q^{6} + 76 q^{7} - 480 q^{8} + 26448 q^{9} - 35 q^{11} + 176 q^{12} + 1049 q^{13} + 636 q^{14} + 82364 q^{16} - 1105 q^{17} + 1348 q^{18} + 3798 q^{19} + 2056 q^{21} - 378 q^{22} + 3785 q^{23} - 12750 q^{24} + 14130 q^{26} + 3556 q^{27} - 18016 q^{28} - 16000 q^{29} - 827 q^{31} - 1676 q^{32} - 15294 q^{33} - 55578 q^{34} + 463186 q^{36} - 1938 q^{37} - 20146 q^{38} - 25558 q^{39} - 59273 q^{41} - 34624 q^{42} + 3698 q^{43} + 41744 q^{44} + 14706 q^{46} + 21316 q^{47} + 44208 q^{48} + 828728 q^{49} + 27566 q^{51} + 35352 q^{52} + 59829 q^{53} + 27308 q^{54} - 102896 q^{56} - 28832 q^{57} - 87594 q^{58} - 125160 q^{59} + 6312 q^{61} - 135238 q^{62} - 259248 q^{63} + 1132760 q^{64} - 123696 q^{66} + 10783 q^{67} - 49610 q^{68} + 362390 q^{69} + 124174 q^{71} - 130740 q^{72} - 65792 q^{73} - 96582 q^{74} + 876 q^{76} + 67792 q^{77} - 197464 q^{78} - 14488 q^{79} + 2070932 q^{81} - 133078 q^{82} - 89527 q^{83} + 441780 q^{84} - 36980 q^{86} - 130280 q^{87} + 138636 q^{88} - 135454 q^{89} + 7016 q^{91} - 209026 q^{92} + 87350 q^{93} + 558676 q^{94} + 62554 q^{96} - 267163 q^{97} + 388176 q^{98} - 512187 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(1075))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 43
1075.6.a.a 1075.a 1.a $8$ $172.413$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(12\) \(26\) \(0\) \(136\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(2+\beta _{1}-\beta _{4}+\beta _{7})q^{3}+\cdots\)
1075.6.a.b 1075.a 1.a $10$ $172.413$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-8\) \(-28\) \(0\) \(-60\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-3-\beta _{6})q^{3}+(21+\cdots)q^{4}+\cdots\)
1075.6.a.c 1075.a 1.a $13$ $172.413$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(7\) \(16\) \(0\) \(372\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(9+\beta _{2}+\cdots)q^{4}+\cdots\)
1075.6.a.d 1075.a 1.a $15$ $172.413$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(5\) \(20\) \(0\) \(118\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{6})q^{3}+(14+\beta _{2})q^{4}+\cdots\)
1075.6.a.e 1075.a 1.a $20$ $172.413$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-7\) \(-16\) \(0\) \(-372\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(17+\beta _{1}+\cdots)q^{4}+\cdots\)
1075.6.a.f 1075.a 1.a $22$ $172.413$ None \(-5\) \(-20\) \(0\) \(-118\) $+$ $-$ $\mathrm{SU}(2)$
1075.6.a.g 1075.a 1.a $33$ $172.413$ None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$
1075.6.a.h 1075.a 1.a $33$ $172.413$ None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$
1075.6.a.i 1075.a 1.a $37$ $172.413$ None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$
1075.6.a.j 1075.a 1.a $37$ $172.413$ None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$
1075.6.a.k 1075.a 1.a $52$ $172.413$ None \(-20\) \(-54\) \(0\) \(-196\) $-$ $-$ $\mathrm{SU}(2)$
1075.6.a.l 1075.a 1.a $52$ $172.413$ None \(20\) \(54\) \(0\) \(196\) $-$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(1075))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(1075)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 2}\)