Properties

Label 1815.4.a
Level $1815$
Weight $4$
Character orbit 1815.a
Rep. character $\chi_{1815}(1,\cdot)$
Character field $\Q$
Dimension $218$
Newform subspaces $41$
Sturm bound $1056$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 41 \)
Sturm bound: \(1056\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1815))\).

Total New Old
Modular forms 816 218 598
Cusp forms 768 218 550
Eisenstein series 48 0 48

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.
\(+\)\(+\)\(+\)\(+\)\(28\)
\(+\)\(+\)\(-\)\(-\)\(27\)
\(+\)\(-\)\(+\)\(-\)\(22\)
\(+\)\(-\)\(-\)\(+\)\(32\)
\(-\)\(+\)\(+\)\(-\)\(26\)
\(-\)\(+\)\(-\)\(+\)\(28\)
\(-\)\(-\)\(+\)\(+\)\(32\)
\(-\)\(-\)\(-\)\(-\)\(23\)
Plus space\(+\)\(120\)
Minus space\(-\)\(98\)

Trace form

\( 218q - 4q^{2} + 898q^{4} - 6q^{6} - 60q^{7} + 36q^{8} + 1962q^{9} + O(q^{10}) \) \( 218q - 4q^{2} + 898q^{4} - 6q^{6} - 60q^{7} + 36q^{8} + 1962q^{9} - 50q^{10} - 24q^{12} - 40q^{13} - 36q^{14} + 30q^{15} + 3514q^{16} + 88q^{17} - 36q^{18} - 8q^{19} + 40q^{20} - 132q^{21} + 272q^{23} - 342q^{24} + 5450q^{25} + 756q^{26} - 164q^{28} - 88q^{29} - 60q^{30} - 64q^{31} + 164q^{32} - 364q^{34} + 300q^{35} + 8082q^{36} - 568q^{37} + 496q^{38} - 180q^{39} - 450q^{40} + 204q^{41} + 588q^{42} + 880q^{43} - 736q^{46} - 648q^{47} - 912q^{48} + 11298q^{49} - 100q^{50} - 300q^{51} + 112q^{52} - 256q^{53} - 54q^{54} + 540q^{56} - 144q^{57} + 3116q^{58} - 156q^{59} - 90q^{60} - 1116q^{61} + 4816q^{62} - 540q^{63} + 15938q^{64} + 580q^{65} + 392q^{67} + 984q^{68} + 1152q^{69} + 980q^{70} + 2440q^{71} + 324q^{72} - 2548q^{73} + 4868q^{74} - 560q^{76} + 168q^{78} + 672q^{79} + 1200q^{80} + 17658q^{81} - 4416q^{82} + 808q^{83} - 3228q^{84} - 1020q^{85} - 32q^{86} - 60q^{87} - 1804q^{89} - 450q^{90} + 5640q^{91} + 3848q^{92} + 4056q^{93} + 6776q^{94} + 520q^{95} - 2862q^{96} + 3076q^{97} - 2668q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1815))\) 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
1815.4.a.a \(1\) \(107.088\) \(\Q\) None \(-3\) \(-3\) \(-5\) \(-20\) \(+\) \(+\) \(-\) \(q-3q^{2}-3q^{3}+q^{4}-5q^{5}+9q^{6}+\cdots\)
1815.4.a.b \(1\) \(107.088\) \(\Q\) None \(-1\) \(-3\) \(-5\) \(33\) \(+\) \(+\) \(-\) \(q-q^{2}-3q^{3}-7q^{4}-5q^{5}+3q^{6}+\cdots\)
1815.4.a.c \(1\) \(107.088\) \(\Q\) None \(-1\) \(3\) \(-5\) \(-36\) \(-\) \(+\) \(-\) \(q-q^{2}+3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
1815.4.a.d \(1\) \(107.088\) \(\Q\) None \(-1\) \(3\) \(5\) \(-9\) \(-\) \(-\) \(-\) \(q-q^{2}+3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots\)
1815.4.a.e \(1\) \(107.088\) \(\Q\) None \(-1\) \(3\) \(5\) \(24\) \(-\) \(-\) \(-\) \(q-q^{2}+3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots\)
1815.4.a.f \(1\) \(107.088\) \(\Q\) None \(0\) \(-3\) \(-5\) \(-2\) \(+\) \(+\) \(-\) \(q-3q^{3}-8q^{4}-5q^{5}-2q^{7}+9q^{9}+\cdots\)
1815.4.a.g \(1\) \(107.088\) \(\Q\) None \(1\) \(-3\) \(-5\) \(-33\) \(+\) \(+\) \(-\) \(q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
1815.4.a.h \(1\) \(107.088\) \(\Q\) None \(1\) \(3\) \(5\) \(9\) \(-\) \(-\) \(-\) \(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
1815.4.a.i \(2\) \(107.088\) \(\Q(\sqrt{41}) \) None \(-1\) \(6\) \(10\) \(-1\) \(-\) \(-\) \(-\) \(q-\beta q^{2}+3q^{3}+(2+\beta )q^{4}+5q^{5}-3\beta q^{6}+\cdots\)
1815.4.a.j \(2\) \(107.088\) \(\Q(\sqrt{5}) \) None \(0\) \(6\) \(-10\) \(0\) \(-\) \(+\) \(+\) \(q+3q^{3}-8q^{4}-5q^{5}+\beta q^{7}+9q^{9}+\cdots\)
1815.4.a.k \(2\) \(107.088\) \(\Q(\sqrt{3}) \) None \(0\) \(6\) \(-10\) \(0\) \(-\) \(+\) \(+\) \(q+2\beta q^{2}+3q^{3}+4q^{4}-5q^{5}+6\beta q^{6}+\cdots\)
1815.4.a.l \(2\) \(107.088\) \(\Q(\sqrt{3}) \) None \(0\) \(6\) \(10\) \(0\) \(-\) \(-\) \(+\) \(q+2\beta q^{2}+3q^{3}+4q^{4}+5q^{5}+6\beta q^{6}+\cdots\)
1815.4.a.m \(2\) \(107.088\) \(\Q(\sqrt{15}) \) None \(0\) \(6\) \(-10\) \(0\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+3q^{3}+7q^{4}-5q^{5}+3\beta q^{6}+\cdots\)
1815.4.a.n \(2\) \(107.088\) \(\Q(\sqrt{17}) \) None \(1\) \(6\) \(-10\) \(4\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+3q^{3}+(-4+\beta )q^{4}-5q^{5}+\cdots\)
1815.4.a.o \(2\) \(107.088\) \(\Q(\sqrt{41}) \) None \(1\) \(6\) \(10\) \(1\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+3q^{3}+(2+\beta )q^{4}+5q^{5}+3\beta q^{6}+\cdots\)
1815.4.a.p \(3\) \(107.088\) 3.3.788.1 None \(-1\) \(-9\) \(15\) \(16\) \(+\) \(-\) \(-\) \(q-\beta _{2}q^{2}-3q^{3}+(-2-\beta _{1})q^{4}+5q^{5}+\cdots\)
1815.4.a.q \(3\) \(107.088\) 3.3.1957.1 None \(-1\) \(-9\) \(15\) \(-6\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{1}+2\beta _{2})q^{4}+\cdots\)
1815.4.a.r \(3\) \(107.088\) 3.3.47528.1 None \(2\) \(9\) \(-15\) \(-10\) \(-\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+3q^{3}+(10+\beta _{2})q^{4}+\cdots\)
1815.4.a.s \(3\) \(107.088\) 3.3.23612.1 None \(4\) \(-9\) \(-15\) \(4\) \(+\) \(+\) \(-\) \(q+(1+\beta _{1})q^{2}-3q^{3}+(7+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.4.a.t \(4\) \(107.088\) 4.4.1540841.1 None \(-4\) \(12\) \(20\) \(-34\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+3q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots\)
1815.4.a.u \(4\) \(107.088\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-1\) \(-12\) \(-20\) \(-45\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.v \(4\) \(107.088\) 4.4.744012.1 None \(0\) \(-12\) \(20\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(3+\beta _{3})q^{4}+5q^{5}+\cdots\)
1815.4.a.w \(4\) \(107.088\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(1\) \(-12\) \(-20\) \(45\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.x \(5\) \(107.088\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-1\) \(15\) \(-25\) \(14\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.4.a.y \(5\) \(107.088\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(15\) \(-25\) \(-14\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.4.a.z \(6\) \(107.088\) 6.6.7598722752.1 None \(0\) \(-18\) \(30\) \(0\) \(+\) \(-\) \(+\) \(q+(\beta _{1}-\beta _{3})q^{2}-3q^{3}+(2-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1815.4.a.ba \(6\) \(107.088\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-18\) \(-30\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(7+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bb \(6\) \(107.088\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(18\) \(30\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bc \(7\) \(107.088\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(-21\) \(35\) \(16\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bd \(7\) \(107.088\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(-21\) \(35\) \(-16\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.be \(8\) \(107.088\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(24\) \(-40\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{4})q^{4}-5q^{5}+\cdots\)
1815.4.a.bf \(10\) \(107.088\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-30\) \(-50\) \(0\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-3q^{3}+(1+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bg \(12\) \(107.088\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-9\) \(36\) \(-60\) \(-21\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.4.a.bh \(12\) \(107.088\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-7\) \(36\) \(60\) \(-77\) \(-\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.4.a.bi \(12\) \(107.088\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(-36\) \(60\) \(5\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bj \(12\) \(107.088\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(-36\) \(-60\) \(51\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bk \(12\) \(107.088\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(36\) \(60\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bl \(12\) \(107.088\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(-36\) \(60\) \(-5\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bm \(12\) \(107.088\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(-36\) \(-60\) \(-51\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bn \(12\) \(107.088\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(7\) \(36\) \(60\) \(77\) \(-\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.4.a.bo \(12\) \(107.088\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(9\) \(36\) \(-60\) \(21\) \(-\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1815))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1815)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 2}\)