Properties

Label 912.2.a
Level $912$
Weight $2$
Character orbit 912.a
Rep. character $\chi_{912}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $15$
Sturm bound $320$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(320\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(912))\).

Total New Old
Modular forms 172 18 154
Cusp forms 149 18 131
Eisenstein series 23 0 23

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

\(2\)\(3\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(7\)
Minus space\(-\)\(11\)

Trace form

\( 18q + 4q^{5} + 4q^{7} + 18q^{9} + O(q^{10}) \) \( 18q + 4q^{5} + 4q^{7} + 18q^{9} + 8q^{11} + 4q^{13} - 4q^{17} - 6q^{19} - 4q^{23} + 22q^{25} - 12q^{29} + 8q^{33} - 12q^{35} - 12q^{37} + 8q^{39} - 4q^{41} + 12q^{43} + 4q^{45} - 24q^{47} + 26q^{49} - 12q^{53} + 20q^{55} + 8q^{59} + 4q^{61} + 4q^{63} - 24q^{65} + 8q^{67} + 40q^{71} - 12q^{73} + 16q^{75} - 16q^{77} - 16q^{79} + 18q^{81} - 12q^{83} + 8q^{85} + 12q^{87} - 20q^{89} + 56q^{91} - 12q^{97} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(912))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 19
912.2.a.a \(1\) \(7.282\) \(\Q\) None \(0\) \(-1\) \(-3\) \(3\) \(+\) \(+\) \(+\) \(q-q^{3}-3q^{5}+3q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
912.2.a.b \(1\) \(7.282\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots\)
912.2.a.c \(1\) \(7.282\) \(\Q\) None \(0\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q-q^{3}+4q^{7}+q^{9}-4q^{13}+6q^{17}+\cdots\)
912.2.a.d \(1\) \(7.282\) \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{5}-3q^{7}+q^{9}+3q^{11}-6q^{13}+\cdots\)
912.2.a.e \(1\) \(7.282\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
912.2.a.f \(1\) \(7.282\) \(\Q\) None \(0\) \(1\) \(-3\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{3}-3q^{5}-q^{7}+q^{9}+5q^{11}-6q^{13}+\cdots\)
912.2.a.g \(1\) \(7.282\) \(\Q\) None \(0\) \(1\) \(-3\) \(5\) \(-\) \(-\) \(-\) \(q+q^{3}-3q^{5}+5q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
912.2.a.h \(1\) \(7.282\) \(\Q\) None \(0\) \(1\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{3}-4q^{7}+q^{9}-4q^{11}-2q^{17}+\cdots\)
912.2.a.i \(1\) \(7.282\) \(\Q\) None \(0\) \(1\) \(1\) \(3\) \(+\) \(-\) \(+\) \(q+q^{3}+q^{5}+3q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots\)
912.2.a.j \(1\) \(7.282\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
912.2.a.k \(1\) \(7.282\) \(\Q\) None \(0\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
912.2.a.l \(1\) \(7.282\) \(\Q\) None \(0\) \(1\) \(4\) \(-4\) \(+\) \(-\) \(+\) \(q+q^{3}+4q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
912.2.a.m \(2\) \(7.282\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
912.2.a.n \(2\) \(7.282\) \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots\)
912.2.a.o \(2\) \(7.282\) \(\Q(\sqrt{41}) \) None \(0\) \(2\) \(-1\) \(3\) \(+\) \(-\) \(+\) \(q+q^{3}-\beta q^{5}+(2-\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(912))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(912)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 2}\)