Properties

Label 1815.2.a
Level $1815$
Weight $2$
Character orbit 1815.a
Rep. character $\chi_{1815}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $25$
Sturm bound $528$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(528\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1815))\).

Total New Old
Modular forms 288 72 216
Cusp forms 241 72 169
Eisenstein series 47 0 47

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

\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(14\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(13\)
Plus space\(+\)\(25\)
Minus space\(-\)\(47\)

Trace form

\( 72q + 4q^{2} - 2q^{3} + 72q^{4} - 2q^{6} + 12q^{8} + 72q^{9} + O(q^{10}) \) \( 72q + 4q^{2} - 2q^{3} + 72q^{4} - 2q^{6} + 12q^{8} + 72q^{9} - 6q^{12} + 24q^{14} - 2q^{15} + 80q^{16} + 8q^{17} + 4q^{18} - 8q^{19} + 8q^{20} - 8q^{21} + 16q^{23} + 6q^{24} + 72q^{25} - 2q^{27} - 8q^{28} + 16q^{29} + 2q^{30} + 8q^{31} + 28q^{32} + 48q^{34} + 72q^{36} + 8q^{37} + 8q^{38} - 4q^{39} + 16q^{42} - 8q^{46} + 24q^{47} + 2q^{48} + 88q^{49} + 4q^{50} - 4q^{51} + 56q^{52} + 40q^{53} - 2q^{54} + 24q^{56} - 16q^{57} + 8q^{58} + 24q^{59} - 6q^{60} + 16q^{61} - 40q^{62} + 88q^{64} + 8q^{65} - 16q^{67} - 48q^{68} + 16q^{70} + 8q^{71} + 12q^{72} - 8q^{74} - 2q^{75} - 24q^{76} + 20q^{78} + 8q^{79} + 72q^{81} + 16q^{82} - 16q^{83} + 16q^{84} - 8q^{85} - 16q^{86} + 4q^{87} + 64q^{89} - 40q^{91} + 16q^{92} - 72q^{93} - 8q^{94} - 16q^{95} + 30q^{96} - 56q^{97} - 68q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1815))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 11
1815.2.a.a \(1\) \(14.493\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
1815.2.a.b \(1\) \(14.493\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}-2q^{12}+\cdots\)
1815.2.a.c \(1\) \(14.493\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-2q^{12}+\cdots\)
1815.2.a.d \(1\) \(14.493\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-3q^{8}+\cdots\)
1815.2.a.e \(1\) \(14.493\) \(\Q\) None \(1\) \(1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
1815.2.a.f \(2\) \(14.493\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(-\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots\)
1815.2.a.g \(2\) \(14.493\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{4}-q^{5}-\beta q^{7}+q^{9}+2q^{12}+\cdots\)
1815.2.a.h \(2\) \(14.493\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
1815.2.a.i \(2\) \(14.493\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(-4\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+q^{3}+q^{4}-q^{5}+\beta q^{6}-2q^{7}+\cdots\)
1815.2.a.j \(2\) \(14.493\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(-2\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
1815.2.a.k \(2\) \(14.493\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(4\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
1815.2.a.l \(3\) \(14.493\) 3.3.469.1 None \(-1\) \(3\) \(3\) \(-3\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1815.2.a.m \(3\) \(14.493\) 3.3.148.1 None \(1\) \(3\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
1815.2.a.n \(3\) \(14.493\) 3.3.469.1 None \(1\) \(3\) \(3\) \(3\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
1815.2.a.o \(4\) \(14.493\) 4.4.725.1 None \(-5\) \(4\) \(-4\) \(2\) \(-\) \(+\) \(-\) \(q+(-2+\beta _{1}+\beta _{2})q^{2}+q^{3}+(3-\beta _{1}+\cdots)q^{4}+\cdots\)
1815.2.a.p \(4\) \(14.493\) 4.4.725.1 None \(-3\) \(4\) \(4\) \(-6\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.2.a.q \(4\) \(14.493\) \(\Q(\zeta_{15})^+\) None \(-1\) \(-4\) \(4\) \(0\) \(+\) \(-\) \(-\) \(q+(\beta _{2}+\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+q^{5}+\cdots\)
1815.2.a.r \(4\) \(14.493\) 4.4.5725.1 None \(-1\) \(-4\) \(-4\) \(8\) \(+\) \(+\) \(-\) \(q+(\beta _{1}-\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
1815.2.a.s \(4\) \(14.493\) 4.4.8112.1 None \(0\) \(-4\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{3})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
1815.2.a.t \(4\) \(14.493\) \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(4\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{3}q^{2}+q^{3}-\beta _{2}q^{4}-q^{5}+\beta _{3}q^{6}+\cdots\)
1815.2.a.u \(4\) \(14.493\) \(\Q(\zeta_{15})^+\) None \(1\) \(-4\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q+(-\beta _{2}-\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+q^{5}+\cdots\)
1815.2.a.v \(4\) \(14.493\) 4.4.5725.1 None \(1\) \(-4\) \(-4\) \(-8\) \(+\) \(+\) \(+\) \(q+(-\beta _{1}+\beta _{2})q^{2}-q^{3}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots\)
1815.2.a.w \(4\) \(14.493\) 4.4.725.1 None \(3\) \(4\) \(4\) \(6\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.2.a.x \(4\) \(14.493\) 4.4.725.1 None \(5\) \(4\) \(-4\) \(-2\) \(-\) \(+\) \(+\) \(q+(2-\beta _{1}-\beta _{2})q^{2}+q^{3}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
1815.2.a.y \(6\) \(14.493\) 6.6.437199552.1 None \(0\) \(-6\) \(6\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1815))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1815)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 2}\)