Properties

Label 1175.4.a
Level 1175
Weight 4
Character orbit a
Rep. character \(\chi_{1175}(1,\cdot)\)
Character field \(\Q\)
Dimension 219
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 12 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1175))\) into newform subspaces

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 \(-3\) \(-7\) \(0\) \(-39\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(5+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1175.4.a.c \(8\) \(69.327\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(10\) \(0\) \(15\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(2-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1175.4.a.d \(10\) \(69.327\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-7\) \(-8\) \(0\) \(-9\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{6})q^{3}+(4+\cdots)q^{4}+\cdots\)
1175.4.a.e \(13\) \(69.327\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(3\) \(10\) \(0\) \(19\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
1175.4.a.f \(15\) \(69.327\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-7\) \(-8\) \(0\) \(-13\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(5+\beta _{2})q^{4}+\cdots\)
1175.4.a.g \(18\) \(69.327\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-1\) \(-7\) \(0\) \(-6\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1175.4.a.h \(18\) \(69.327\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(1\) \(7\) \(0\) \(6\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
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

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