Properties

Label 475.2.a
Level $475$
Weight $2$
Character orbit 475.a
Rep. character $\chi_{475}(1,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $10$
Sturm bound $100$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(100\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(475))\).

Total New Old
Modular forms 56 28 28
Cusp forms 45 28 17
Eisenstein series 11 0 11

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

\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(11\)
Minus space\(-\)\(17\)

Trace form

\( 28q + q^{2} - 2q^{3} + 29q^{4} - 3q^{7} + 9q^{8} + 16q^{9} + O(q^{10}) \) \( 28q + q^{2} - 2q^{3} + 29q^{4} - 3q^{7} + 9q^{8} + 16q^{9} - 3q^{11} - 6q^{13} + 23q^{16} - 3q^{17} + 29q^{18} - 2q^{19} - 6q^{21} + 12q^{22} + 12q^{23} + 8q^{24} + 6q^{26} - 8q^{27} - 6q^{28} - 16q^{31} + 9q^{32} - 6q^{33} - 10q^{34} - 27q^{36} - 16q^{37} + 3q^{38} - 28q^{39} + 4q^{41} - 16q^{42} + q^{43} - 2q^{44} + 4q^{46} + 15q^{47} - 40q^{48} - 13q^{49} - 2q^{51} - 30q^{52} - 18q^{53} - 52q^{54} - 32q^{56} + 2q^{57} - 2q^{58} + 2q^{59} - 21q^{61} - 48q^{62} + 13q^{63} + 79q^{64} - 36q^{66} + 20q^{67} - 8q^{68} + 18q^{71} + 65q^{72} - 23q^{73} - 2q^{74} - 5q^{76} + 35q^{77} - 24q^{79} + 16q^{81} + 2q^{82} + 20q^{83} - 56q^{84} + 40q^{86} + 76q^{87} + 16q^{88} + 2q^{89} - 24q^{91} + 20q^{92} + 48q^{93} + 24q^{94} - 52q^{96} - 58q^{97} - 23q^{98} + 9q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(475))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 19
475.2.a.a \(1\) \(3.793\) \(\Q\) None \(-1\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q-q^{2}-q^{4}+2q^{7}+3q^{8}-3q^{9}-4q^{11}+\cdots\)
475.2.a.b \(1\) \(3.793\) \(\Q\) None \(0\) \(2\) \(0\) \(1\) \(+\) \(-\) \(q+2q^{3}-2q^{4}+q^{7}+q^{9}+3q^{11}+\cdots\)
475.2.a.c \(1\) \(3.793\) \(\Q\) None \(1\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(q+q^{2}-q^{4}-2q^{7}-3q^{8}-3q^{9}-4q^{11}+\cdots\)
475.2.a.d \(3\) \(3.793\) \(\Q(\zeta_{14})^+\) None \(-4\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
475.2.a.e \(3\) \(3.793\) 3.3.169.1 None \(-2\) \(-2\) \(0\) \(-4\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
475.2.a.f \(3\) \(3.793\) 3.3.148.1 None \(-1\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
475.2.a.g \(3\) \(3.793\) 3.3.169.1 None \(2\) \(2\) \(0\) \(4\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
475.2.a.h \(3\) \(3.793\) \(\Q(\zeta_{14})^+\) None \(4\) \(2\) \(0\) \(0\) \(-\) \(+\) \(q+(1+\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
475.2.a.i \(4\) \(3.793\) 4.4.11344.1 None \(2\) \(-2\) \(0\) \(-4\) \(+\) \(-\) \(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
475.2.a.j \(6\) \(3.793\) 6.6.66064384.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(475))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(475)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 2}\)