Properties

Label 930.2.a
Level $930$
Weight $2$
Character orbit 930.a
Rep. character $\chi_{930}(1,\cdot)$
Character field $\Q$
Dimension $21$
Newform subspaces $18$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(930))\).

Total New Old
Modular forms 200 21 179
Cusp forms 185 21 164
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.

\(2\)\(3\)\(5\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(16\)

Trace form

\( 21q + q^{2} + q^{3} + 21q^{4} + q^{5} + q^{6} + 8q^{7} + q^{8} + 21q^{9} + O(q^{10}) \) \( 21q + q^{2} + q^{3} + 21q^{4} + q^{5} + q^{6} + 8q^{7} + q^{8} + 21q^{9} - 3q^{10} + 4q^{11} + q^{12} + 14q^{13} + q^{15} + 21q^{16} + 2q^{17} + q^{18} - 4q^{19} + q^{20} + 8q^{21} + 12q^{22} + 8q^{23} + q^{24} + 21q^{25} + 6q^{26} + q^{27} + 8q^{28} + 14q^{29} + q^{30} + q^{31} + q^{32} + 4q^{33} + 2q^{34} + 21q^{36} + 6q^{37} + 20q^{38} + 14q^{39} - 3q^{40} + 18q^{41} - 8q^{42} + 28q^{43} + 4q^{44} + q^{45} + 16q^{46} - 16q^{47} + q^{48} + 5q^{49} + q^{50} + 2q^{51} + 14q^{52} + 6q^{53} + q^{54} - 4q^{55} + 20q^{57} + 14q^{58} - 12q^{59} + q^{60} + 14q^{61} + q^{62} + 8q^{63} + 21q^{64} - 10q^{65} + 12q^{66} + 12q^{67} + 2q^{68} - 24q^{69} - 40q^{71} + q^{72} - 6q^{73} + 14q^{74} + q^{75} - 4q^{76} - 32q^{77} + 6q^{78} - 48q^{79} + q^{80} + 21q^{81} - 6q^{82} - 76q^{83} + 8q^{84} + 18q^{85} - 4q^{86} - 2q^{87} + 12q^{88} - 62q^{89} - 3q^{90} - 32q^{91} + 8q^{92} - 3q^{93} + 16q^{94} - 28q^{95} + q^{96} - 22q^{97} - 7q^{98} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(930))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 31
930.2.a.a \(1\) \(7.426\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
930.2.a.b \(1\) \(7.426\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
930.2.a.c \(1\) \(7.426\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots\)
930.2.a.d \(1\) \(7.426\) \(\Q\) None \(-1\) \(-1\) \(1\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
930.2.a.e \(1\) \(7.426\) \(\Q\) None \(-1\) \(-1\) \(1\) \(3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
930.2.a.f \(1\) \(7.426\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
930.2.a.g \(1\) \(7.426\) \(\Q\) None \(-1\) \(1\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
930.2.a.h \(1\) \(7.426\) \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
930.2.a.i \(1\) \(7.426\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
930.2.a.j \(1\) \(7.426\) \(\Q\) None \(-1\) \(1\) \(1\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
930.2.a.k \(1\) \(7.426\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
930.2.a.l \(1\) \(7.426\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
930.2.a.m \(1\) \(7.426\) \(\Q\) None \(1\) \(-1\) \(-1\) \(3\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
930.2.a.n \(1\) \(7.426\) \(\Q\) None \(1\) \(1\) \(-1\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
930.2.a.o \(1\) \(7.426\) \(\Q\) None \(1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
930.2.a.p \(2\) \(7.426\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(2\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+\beta q^{7}+\cdots\)
930.2.a.q \(2\) \(7.426\) \(\Q(\sqrt{65}) \) None \(2\) \(2\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-\beta q^{7}+\cdots\)
930.2.a.r \(2\) \(7.426\) \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(930))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(930)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 2}\)