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

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

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

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