Properties

Label 1175.4.a
Level 1175
Weight 4
Character orbit a
Rep. character \(\chi_{1175}(1,\cdot)\)
Character field \(\Q\)
Dimension 219
Newforms 12
Sturm bound 480
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1175 = 5^{2} \cdot 47 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 1175.a (trivial)
Character field: \(\Q\)
Newforms: \( 12 \)
Sturm bound: \(480\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1175))\).

Total New Old
Modular forms 366 219 147
Cusp forms 354 219 135
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.

\(5\)\(47\)FrickeDim.
\(+\)\(+\)\(+\)\(59\)
\(+\)\(-\)\(-\)\(44\)
\(-\)\(+\)\(-\)\(53\)
\(-\)\(-\)\(+\)\(63\)
Plus space\(+\)\(122\)
Minus space\(-\)\(97\)

Trace form

\(219q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 890q^{4} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut -\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 1959q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(219q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 890q^{4} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut -\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 1959q^{9} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 40q^{13} \) \(\mathstrut +\mathstrut 205q^{14} \) \(\mathstrut +\mathstrut 3538q^{16} \) \(\mathstrut +\mathstrut 138q^{17} \) \(\mathstrut +\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 70q^{19} \) \(\mathstrut -\mathstrut 64q^{21} \) \(\mathstrut +\mathstrut 218q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 863q^{24} \) \(\mathstrut -\mathstrut 476q^{26} \) \(\mathstrut +\mathstrut 56q^{27} \) \(\mathstrut +\mathstrut 660q^{28} \) \(\mathstrut -\mathstrut 496q^{29} \) \(\mathstrut -\mathstrut 132q^{31} \) \(\mathstrut +\mathstrut 339q^{32} \) \(\mathstrut +\mathstrut 432q^{33} \) \(\mathstrut -\mathstrut 216q^{34} \) \(\mathstrut +\mathstrut 7618q^{36} \) \(\mathstrut +\mathstrut 566q^{37} \) \(\mathstrut -\mathstrut 820q^{38} \) \(\mathstrut +\mathstrut 460q^{39} \) \(\mathstrut +\mathstrut 226q^{41} \) \(\mathstrut +\mathstrut 463q^{42} \) \(\mathstrut +\mathstrut 402q^{43} \) \(\mathstrut -\mathstrut 1316q^{44} \) \(\mathstrut -\mathstrut 874q^{46} \) \(\mathstrut -\mathstrut 235q^{47} \) \(\mathstrut -\mathstrut 860q^{48} \) \(\mathstrut +\mathstrut 10855q^{49} \) \(\mathstrut -\mathstrut 222q^{51} \) \(\mathstrut -\mathstrut 60q^{52} \) \(\mathstrut +\mathstrut 454q^{53} \) \(\mathstrut +\mathstrut 1125q^{54} \) \(\mathstrut +\mathstrut 3244q^{56} \) \(\mathstrut +\mathstrut 764q^{57} \) \(\mathstrut +\mathstrut 520q^{58} \) \(\mathstrut +\mathstrut 162q^{59} \) \(\mathstrut +\mathstrut 2542q^{61} \) \(\mathstrut +\mathstrut 324q^{62} \) \(\mathstrut +\mathstrut 1628q^{63} \) \(\mathstrut +\mathstrut 14134q^{64} \) \(\mathstrut +\mathstrut 2068q^{66} \) \(\mathstrut +\mathstrut 658q^{67} \) \(\mathstrut +\mathstrut 2113q^{68} \) \(\mathstrut -\mathstrut 1532q^{69} \) \(\mathstrut +\mathstrut 522q^{71} \) \(\mathstrut -\mathstrut 1254q^{72} \) \(\mathstrut -\mathstrut 2462q^{73} \) \(\mathstrut +\mathstrut 3064q^{74} \) \(\mathstrut -\mathstrut 3750q^{76} \) \(\mathstrut +\mathstrut 1556q^{77} \) \(\mathstrut -\mathstrut 824q^{78} \) \(\mathstrut -\mathstrut 1498q^{79} \) \(\mathstrut +\mathstrut 20595q^{81} \) \(\mathstrut +\mathstrut 2126q^{82} \) \(\mathstrut +\mathstrut 1440q^{83} \) \(\mathstrut -\mathstrut 1199q^{84} \) \(\mathstrut +\mathstrut 2036q^{86} \) \(\mathstrut -\mathstrut 4408q^{87} \) \(\mathstrut +\mathstrut 2920q^{88} \) \(\mathstrut +\mathstrut 3398q^{89} \) \(\mathstrut +\mathstrut 1508q^{91} \) \(\mathstrut +\mathstrut 84q^{92} \) \(\mathstrut +\mathstrut 6484q^{93} \) \(\mathstrut +\mathstrut 376q^{94} \) \(\mathstrut -\mathstrut 1484q^{96} \) \(\mathstrut +\mathstrut 2738q^{97} \) \(\mathstrut -\mathstrut 2234q^{98} \) \(\mathstrut +\mathstrut 5542q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1175))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 47
1175.4.a.a \(3\) \(69.327\) 3.3.1101.1 None \(5\) \(5\) \(0\) \(45\) \(+\) \(+\) \(q+(2+\beta _{2})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
1175.4.a.b \(8\) \(69.327\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-3\) \(-7\) \(0\) \(-39\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(5-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1175.4.a.c \(8\) \(69.327\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(10\) \(0\) \(15\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(2-\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1175.4.a.d \(10\) \(69.327\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-7\) \(-8\) \(0\) \(-9\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)
1175.4.a.e \(13\) \(69.327\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(3\) \(10\) \(0\) \(19\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(4+\beta _{5})q^{4}+\cdots\)
1175.4.a.f \(15\) \(69.327\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-7\) \(-8\) \(0\) \(-13\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(5+\beta _{3})q^{4}+\cdots\)
1175.4.a.g \(18\) \(69.327\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-1\) \(-7\) \(0\) \(-6\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(3+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1175.4.a.h \(18\) \(69.327\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(1\) \(7\) \(0\) \(6\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(3+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1175.4.a.i \(28\) \(69.327\) None \(-1\) \(-7\) \(0\) \(-6\) \(+\) \(+\)
1175.4.a.j \(28\) \(69.327\) None \(1\) \(7\) \(0\) \(6\) \(-\) \(-\)
1175.4.a.k \(35\) \(69.327\) None \(-8\) \(-12\) \(0\) \(-84\) \(-\) \(+\)
1175.4.a.l \(35\) \(69.327\) None \(8\) \(12\) \(0\) \(84\) \(-\) \(-\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1175))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1175)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(235))\)\(^{\oplus 2}\)