Properties

Label 1122.2.a
Level $1122$
Weight $2$
Character orbit 1122.a
Rep. character $\chi_{1122}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $19$
Sturm bound $432$
Trace bound $13$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1122.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(432\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1122))\).

Total New Old
Modular forms 224 25 199
Cusp forms 209 25 184
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.

\(2\)\(3\)\(11\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(9\)
Minus space\(-\)\(16\)

Trace form

\( 25q + q^{2} - 3q^{3} + 25q^{4} + 6q^{5} + q^{6} + q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + q^{2} - 3q^{3} + 25q^{4} + 6q^{5} + q^{6} + q^{8} + 25q^{9} + 6q^{10} + q^{11} - 3q^{12} + 6q^{13} + 8q^{14} + 6q^{15} + 25q^{16} + q^{17} + q^{18} - 4q^{19} + 6q^{20} - 16q^{21} - 3q^{22} - 16q^{23} + q^{24} + 7q^{25} + 6q^{26} - 3q^{27} - 2q^{29} + 6q^{30} + q^{32} + q^{33} - 7q^{34} + 25q^{36} + 6q^{37} - 20q^{38} - 26q^{39} + 6q^{40} + 10q^{41} + 8q^{42} - 44q^{43} + q^{44} + 6q^{45} + 8q^{46} + 16q^{47} - 3q^{48} + 33q^{49} + 15q^{50} + q^{51} + 6q^{52} - 18q^{53} + q^{54} + 6q^{55} + 8q^{56} - 4q^{57} + 14q^{58} - 12q^{59} + 6q^{60} - 10q^{61} + 25q^{64} + 20q^{65} + q^{66} + 4q^{67} + q^{68} + 8q^{69} + 32q^{70} + 16q^{71} + q^{72} + 34q^{73} + 22q^{74} + 3q^{75} - 4q^{76} + 6q^{78} - 56q^{79} + 6q^{80} + 25q^{81} + 10q^{82} + 4q^{83} - 16q^{84} + 6q^{85} - 12q^{86} - 2q^{87} - 3q^{88} + 42q^{89} + 6q^{90} + 16q^{91} - 16q^{92} + 8q^{93} + 16q^{94} + 8q^{95} + q^{96} - 14q^{97} - 23q^{98} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1122))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11 17
1122.2.a.a \(1\) \(8.959\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
1122.2.a.b \(1\) \(8.959\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.c \(1\) \(8.959\) \(\Q\) None \(-1\) \(-1\) \(2\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.d \(1\) \(8.959\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.e \(1\) \(8.959\) \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.f \(1\) \(8.959\) \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.g \(1\) \(8.959\) \(\Q\) None \(1\) \(-1\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.h \(1\) \(8.959\) \(\Q\) None \(1\) \(-1\) \(2\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
1122.2.a.i \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(-2\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
1122.2.a.j \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.k \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.l \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.m \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(2\) \(4\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.n \(1\) \(8.959\) \(\Q\) None \(1\) \(1\) \(4\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.o \(2\) \(8.959\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(6\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
1122.2.a.p \(2\) \(8.959\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
1122.2.a.q \(2\) \(8.959\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
1122.2.a.r \(2\) \(8.959\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
1122.2.a.s \(3\) \(8.959\) 3.3.148.1 None \(3\) \(-3\) \(0\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1122))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1122)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(374))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 2}\)