Properties

Label 1911.2.a
Level $1911$
Weight $2$
Character orbit 1911.a
Rep. character $\chi_{1911}(1,\cdot)$
Character field $\Q$
Dimension $82$
Newform subspaces $25$
Sturm bound $522$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1911.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(522\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1911))\).

Total New Old
Modular forms 276 82 194
Cusp forms 245 82 163
Eisenstein series 31 0 31

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

\(3\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(13\)
\(+\)\(-\)\(+\)\(-\)\(12\)
\(+\)\(-\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(27\)
Minus space\(-\)\(55\)

Trace form

\( 82q + 4q^{2} + 82q^{4} + 4q^{5} - 2q^{6} + 24q^{8} + 82q^{9} + O(q^{10}) \) \( 82q + 4q^{2} + 82q^{4} + 4q^{5} - 2q^{6} + 24q^{8} + 82q^{9} + 8q^{10} + 12q^{11} - 4q^{12} + 2q^{13} + 78q^{16} + 4q^{17} + 4q^{18} - 4q^{19} + 28q^{20} + 20q^{22} + 24q^{23} - 6q^{24} + 110q^{25} + 28q^{29} + 20q^{30} + 12q^{31} + 52q^{32} + 12q^{33} + 24q^{34} + 82q^{36} + 20q^{37} - 4q^{38} - 4q^{39} - 4q^{41} + 16q^{43} + 36q^{44} + 4q^{45} + 16q^{46} + 12q^{47} + 8q^{48} + 12q^{50} - 8q^{51} + 2q^{52} + 28q^{53} - 2q^{54} - 4q^{57} + 24q^{58} + 20q^{59} - 20q^{61} - 12q^{62} + 122q^{64} + 4q^{65} + 12q^{66} + 12q^{67} + 44q^{68} - 8q^{69} - 4q^{71} + 24q^{72} - 12q^{73} + 88q^{74} - 24q^{75} + 44q^{76} - 2q^{78} + 24q^{79} + 52q^{80} + 82q^{81} - 24q^{82} + 4q^{83} + 32q^{85} - 128q^{86} - 8q^{87} - 12q^{88} + 4q^{89} + 8q^{90} - 128q^{92} + 4q^{93} - 44q^{94} + 24q^{95} - 34q^{96} + 20q^{97} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1911))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 13
1911.2.a.a \(1\) \(15.259\) \(\Q\) None \(-2\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots\)
1911.2.a.b \(1\) \(15.259\) \(\Q\) None \(-1\) \(-1\) \(-4\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}-q^{4}-4q^{5}+q^{6}+3q^{8}+\cdots\)
1911.2.a.c \(1\) \(15.259\) \(\Q\) None \(-1\) \(1\) \(4\) \(0\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}+4q^{5}-q^{6}+3q^{8}+\cdots\)
1911.2.a.d \(1\) \(15.259\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}-q^{5}+q^{9}-2q^{11}+2q^{12}+\cdots\)
1911.2.a.e \(1\) \(15.259\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{4}+q^{5}+q^{9}-2q^{11}-2q^{12}+\cdots\)
1911.2.a.f \(1\) \(15.259\) \(\Q\) None \(1\) \(1\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
1911.2.a.g \(1\) \(15.259\) \(\Q\) None \(2\) \(-1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
1911.2.a.h \(2\) \(15.259\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
1911.2.a.i \(2\) \(15.259\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(+\) \(q+\beta q^{2}-q^{3}+q^{5}-\beta q^{6}-2\beta q^{8}+\cdots\)
1911.2.a.j \(2\) \(15.259\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+q^{3}-q^{5}+\beta q^{6}-2\beta q^{8}+\cdots\)
1911.2.a.k \(2\) \(15.259\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
1911.2.a.l \(3\) \(15.259\) \(\Q(\zeta_{14})^+\) None \(-2\) \(-3\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.2.a.m \(3\) \(15.259\) \(\Q(\zeta_{14})^+\) None \(-2\) \(3\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.2.a.n \(3\) \(15.259\) 3.3.316.1 None \(-2\) \(3\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.2.a.o \(3\) \(15.259\) \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(3\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+\cdots\)
1911.2.a.p \(3\) \(15.259\) \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1911.2.a.q \(4\) \(15.259\) 4.4.69777.1 None \(-1\) \(-4\) \(-3\) \(0\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1911.2.a.r \(4\) \(15.259\) 4.4.69777.1 None \(-1\) \(4\) \(3\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
1911.2.a.s \(4\) \(15.259\) 4.4.17428.1 None \(1\) \(-4\) \(3\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
1911.2.a.t \(5\) \(15.259\) 5.5.375116.1 None \(0\) \(-5\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{3}q^{2}-q^{3}+(1-\beta _{4})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1911.2.a.u \(5\) \(15.259\) 5.5.375116.1 None \(0\) \(5\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
1911.2.a.v \(5\) \(15.259\) 5.5.2196544.1 None \(2\) \(-5\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
1911.2.a.w \(5\) \(15.259\) 5.5.2196544.1 None \(2\) \(5\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
1911.2.a.x \(10\) \(15.259\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(-10\) \(6\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots\)
1911.2.a.y \(10\) \(15.259\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(4\) \(10\) \(-6\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1911))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1911)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 2}\)