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Properties

Label 608.2.a
Level $608$
Weight $2$
Character orbit 608.a
Rep. character $\chi_{608}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $10$
Sturm bound $160$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 608.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(160\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(608))\).

Total New Old
Modular forms 88 18 70
Cusp forms 73 18 55
Eisenstein series 15 0 15

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

\(2\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(12\)

Trace form

\( 18 q + 4 q^{5} + 18 q^{9} + O(q^{10}) \) \( 18 q + 4 q^{5} + 18 q^{9} + 4 q^{13} - 12 q^{17} + 16 q^{21} + 22 q^{25} + 20 q^{29} + 16 q^{33} + 20 q^{37} - 12 q^{41} - 12 q^{45} + 34 q^{49} - 44 q^{53} + 20 q^{61} - 24 q^{65} + 4 q^{73} + 8 q^{77} - 30 q^{81} - 60 q^{89} - 16 q^{93} - 60 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(608))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19
608.2.a.a \(1\) \(4.855\) \(\Q\) None \(0\) \(-3\) \(0\) \(1\) \(-\) \(-\) \(q-3q^{3}+q^{7}+6q^{9}-2q^{11}-q^{13}+\cdots\)
608.2.a.b \(1\) \(4.855\) \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) \(-\) \(-\) \(q-q^{5}-q^{7}-3q^{9}+3q^{11}-4q^{13}+\cdots\)
608.2.a.c \(1\) \(4.855\) \(\Q\) None \(0\) \(0\) \(-1\) \(1\) \(+\) \(+\) \(q-q^{5}+q^{7}-3q^{9}-3q^{11}-4q^{13}+\cdots\)
608.2.a.d \(1\) \(4.855\) \(\Q\) None \(0\) \(0\) \(3\) \(-5\) \(-\) \(-\) \(q+3q^{5}-5q^{7}-3q^{9}-5q^{11}-4q^{13}+\cdots\)
608.2.a.e \(1\) \(4.855\) \(\Q\) None \(0\) \(0\) \(3\) \(5\) \(-\) \(+\) \(q+3q^{5}+5q^{7}-3q^{9}+5q^{11}-4q^{13}+\cdots\)
608.2.a.f \(1\) \(4.855\) \(\Q\) None \(0\) \(3\) \(0\) \(-1\) \(-\) \(+\) \(q+3q^{3}-q^{7}+6q^{9}+2q^{11}-q^{13}+\cdots\)
608.2.a.g \(2\) \(4.855\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-1\) \(-6\) \(+\) \(+\) \(q-\beta q^{3}+(-1+\beta )q^{5}-3q^{7}+(1+\beta )q^{9}+\cdots\)
608.2.a.h \(2\) \(4.855\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-1\) \(6\) \(+\) \(-\) \(q+\beta q^{3}+(-1+\beta )q^{5}+3q^{7}+(1+\beta )q^{9}+\cdots\)
608.2.a.i \(4\) \(4.855\) 4.4.15317.1 None \(0\) \(-2\) \(1\) \(1\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\cdots\)
608.2.a.j \(4\) \(4.855\) 4.4.15317.1 None \(0\) \(2\) \(1\) \(-1\) \(+\) \(-\) \(q+(1+\beta _{2})q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(608))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(608)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 2}\)