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 $7$

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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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1815))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 11
1815.4.a.a 1815.a 1.a $1$ $107.088$ \(\Q\) None \(-3\) \(-3\) \(-5\) \(-20\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}-3q^{3}+q^{4}-5q^{5}+9q^{6}+\cdots\)
1815.4.a.b 1815.a 1.a $1$ $107.088$ \(\Q\) None \(-1\) \(-3\) \(-5\) \(33\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-7q^{4}-5q^{5}+3q^{6}+\cdots\)
1815.4.a.c 1815.a 1.a $1$ $107.088$ \(\Q\) None \(-1\) \(3\) \(-5\) \(-36\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
1815.4.a.d 1815.a 1.a $1$ $107.088$ \(\Q\) None \(-1\) \(3\) \(5\) \(-9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots\)
1815.4.a.e 1815.a 1.a $1$ $107.088$ \(\Q\) None \(-1\) \(3\) \(5\) \(24\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots\)
1815.4.a.f 1815.a 1.a $1$ $107.088$ \(\Q\) None \(0\) \(-3\) \(-5\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-8q^{4}-5q^{5}-2q^{7}+9q^{9}+\cdots\)
1815.4.a.g 1815.a 1.a $1$ $107.088$ \(\Q\) None \(1\) \(-3\) \(-5\) \(-33\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
1815.4.a.h 1815.a 1.a $1$ $107.088$ \(\Q\) None \(1\) \(3\) \(5\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
1815.4.a.i 1815.a 1.a $2$ $107.088$ \(\Q(\sqrt{41}) \) None \(-1\) \(6\) \(10\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{3}+(2+\beta )q^{4}+5q^{5}-3\beta q^{6}+\cdots\)
1815.4.a.j 1815.a 1.a $2$ $107.088$ \(\Q(\sqrt{5}) \) None \(0\) \(6\) \(-10\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-8q^{4}-5q^{5}+\beta q^{7}+9q^{9}+\cdots\)
1815.4.a.k 1815.a 1.a $2$ $107.088$ \(\Q(\sqrt{3}) \) None \(0\) \(6\) \(-10\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{2}+3q^{3}+4q^{4}-5q^{5}+6\beta q^{6}+\cdots\)
1815.4.a.l 1815.a 1.a $2$ $107.088$ \(\Q(\sqrt{3}) \) None \(0\) \(6\) \(10\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2\beta q^{2}+3q^{3}+4q^{4}+5q^{5}+6\beta q^{6}+\cdots\)
1815.4.a.m 1815.a 1.a $2$ $107.088$ \(\Q(\sqrt{15}) \) None \(0\) \(6\) \(-10\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+7q^{4}-5q^{5}+3\beta q^{6}+\cdots\)
1815.4.a.n 1815.a 1.a $2$ $107.088$ \(\Q(\sqrt{17}) \) None \(1\) \(6\) \(-10\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+(-4+\beta )q^{4}-5q^{5}+\cdots\)
1815.4.a.o 1815.a 1.a $2$ $107.088$ \(\Q(\sqrt{41}) \) None \(1\) \(6\) \(10\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{3}+(2+\beta )q^{4}+5q^{5}+3\beta q^{6}+\cdots\)
1815.4.a.p 1815.a 1.a $3$ $107.088$ 3.3.788.1 None \(-1\) \(-9\) \(15\) \(16\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-3q^{3}+(-2-\beta _{1})q^{4}+5q^{5}+\cdots\)
1815.4.a.q 1815.a 1.a $3$ $107.088$ 3.3.1957.1 None \(-1\) \(-9\) \(15\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{1}+2\beta _{2})q^{4}+\cdots\)
1815.4.a.r 1815.a 1.a $3$ $107.088$ 3.3.47528.1 None \(2\) \(9\) \(-15\) \(-10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(10+\beta _{2})q^{4}+\cdots\)
1815.4.a.s 1815.a 1.a $3$ $107.088$ 3.3.23612.1 None \(4\) \(-9\) \(-15\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}-3q^{3}+(7+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.4.a.t 1815.a 1.a $4$ $107.088$ 4.4.1540841.1 None \(-4\) \(12\) \(20\) \(-34\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots\)
1815.4.a.u 1815.a 1.a $4$ $107.088$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-1\) \(-12\) \(-20\) \(-45\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.v 1815.a 1.a $4$ $107.088$ 4.4.744012.1 None \(0\) \(-12\) \(20\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(3+\beta _{3})q^{4}+5q^{5}+\cdots\)
1815.4.a.w 1815.a 1.a $4$ $107.088$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(1\) \(-12\) \(-20\) \(45\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.x 1815.a 1.a $5$ $107.088$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-1\) \(15\) \(-25\) \(14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.4.a.y 1815.a 1.a $5$ $107.088$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(15\) \(-25\) \(-14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.4.a.z 1815.a 1.a $6$ $107.088$ 6.6.7598722752.1 None \(0\) \(-18\) \(30\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3})q^{2}-3q^{3}+(2-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1815.4.a.ba 1815.a 1.a $6$ $107.088$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-18\) \(-30\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(7+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bb 1815.a 1.a $6$ $107.088$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(18\) \(30\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bc 1815.a 1.a $7$ $107.088$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(-21\) \(35\) \(16\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bd 1815.a 1.a $7$ $107.088$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(-21\) \(35\) \(-16\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.be 1815.a 1.a $8$ $107.088$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(24\) \(-40\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{4})q^{4}-5q^{5}+\cdots\)
1815.4.a.bf 1815.a 1.a $10$ $107.088$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-30\) \(-50\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(1+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bg 1815.a 1.a $12$ $107.088$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-9\) \(36\) \(-60\) \(-21\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.4.a.bh 1815.a 1.a $12$ $107.088$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-7\) \(36\) \(60\) \(-77\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.4.a.bi 1815.a 1.a $12$ $107.088$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(-36\) \(60\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bj 1815.a 1.a $12$ $107.088$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(-36\) \(-60\) \(51\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bk 1815.a 1.a $12$ $107.088$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(36\) \(60\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bl 1815.a 1.a $12$ $107.088$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(-36\) \(60\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bm 1815.a 1.a $12$ $107.088$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(-36\) \(-60\) \(-51\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bn 1815.a 1.a $12$ $107.088$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(7\) \(36\) \(60\) \(77\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.4.a.bo 1815.a 1.a $12$ $107.088$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(9\) \(36\) \(-60\) \(21\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

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

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