Properties

Label 1110.2.a
Level $1110$
Weight $2$
Character orbit 1110.a
Rep. character $\chi_{1110}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $19$
Sturm bound $456$
Trace bound $7$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(456\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1110))\).

Total New Old
Modular forms 236 25 211
Cusp forms 221 25 196
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.

\(2\)\(3\)\(5\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
Plus space\(+\)\(9\)
Minus space\(-\)\(16\)

Trace form

\( 25q + q^{2} + q^{3} + 25q^{4} + q^{5} + q^{6} + 8q^{7} + q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + q^{2} + q^{3} + 25q^{4} + q^{5} + q^{6} + 8q^{7} + q^{8} + 25q^{9} + q^{10} - 4q^{11} + q^{12} - 10q^{13} - 8q^{14} + q^{15} + 25q^{16} - 14q^{17} + q^{18} + 20q^{19} + q^{20} + 8q^{21} - 12q^{22} - 8q^{23} + q^{24} + 25q^{25} - 2q^{26} + q^{27} + 8q^{28} + 14q^{29} + q^{30} + q^{32} + 12q^{33} + 18q^{34} + 8q^{35} + 25q^{36} - 3q^{37} - 20q^{38} + 14q^{39} + q^{40} + 2q^{41} + 4q^{43} - 4q^{44} + q^{45} - 32q^{47} + q^{48} + 33q^{49} + q^{50} + 2q^{51} - 10q^{52} - 34q^{53} + q^{54} + 12q^{55} - 8q^{56} + 12q^{57} - 18q^{58} - 4q^{59} + q^{60} - 2q^{61} + 8q^{62} + 8q^{63} + 25q^{64} - 2q^{65} - 4q^{66} - 12q^{67} - 14q^{68} + 8q^{69} + 8q^{70} - 24q^{71} + q^{72} - 14q^{73} + q^{74} + q^{75} + 20q^{76} - 16q^{77} - 2q^{78} + 32q^{79} + q^{80} + 25q^{81} + 10q^{82} - 28q^{83} + 8q^{84} + 18q^{85} - 12q^{86} + 14q^{87} - 12q^{88} - 6q^{89} + q^{90} - 16q^{91} - 8q^{92} + 8q^{93} + 16q^{94} - 12q^{95} + q^{96} + 2q^{97} - 7q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1110))\) 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 37
1110.2.a.a \(1\) \(8.863\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-4\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots\)
1110.2.a.b \(1\) \(8.863\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
1110.2.a.c \(1\) \(8.863\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots\)
1110.2.a.d \(1\) \(8.863\) \(\Q\) None \(-1\) \(-1\) \(1\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
1110.2.a.e \(1\) \(8.863\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
1110.2.a.f \(1\) \(8.863\) \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
1110.2.a.g \(1\) \(8.863\) \(\Q\) None \(-1\) \(1\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
1110.2.a.h \(1\) \(8.863\) \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
1110.2.a.i \(1\) \(8.863\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
1110.2.a.j \(1\) \(8.863\) \(\Q\) None \(1\) \(-1\) \(1\) \(-3\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots\)
1110.2.a.k \(1\) \(8.863\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
1110.2.a.l \(1\) \(8.863\) \(\Q\) None \(1\) \(-1\) \(1\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
1110.2.a.m \(1\) \(8.863\) \(\Q\) None \(1\) \(1\) \(-1\) \(-5\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-5q^{7}+\cdots\)
1110.2.a.n \(1\) \(8.863\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
1110.2.a.o \(1\) \(8.863\) \(\Q\) None \(1\) \(1\) \(-1\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
1110.2.a.p \(2\) \(8.863\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(2\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta q^{7}+\cdots\)
1110.2.a.q \(2\) \(8.863\) \(\Q(\sqrt{113}) \) None \(-2\) \(2\) \(2\) \(6\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
1110.2.a.r \(2\) \(8.863\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
1110.2.a.s \(4\) \(8.863\) 4.4.54764.1 None \(4\) \(4\) \(4\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1110))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1110)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(555))\)\(^{\oplus 2}\)