Properties

Label 5415.2.a
Level $5415$
Weight $2$
Character orbit 5415.a
Rep. character $\chi_{5415}(1,\cdot)$
Character field $\Q$
Dimension $228$
Newform subspaces $46$
Sturm bound $1520$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5415.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 46 \)
Sturm bound: \(1520\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5415))\).

Total New Old
Modular forms 800 228 572
Cusp forms 721 228 493
Eisenstein series 79 0 79

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

\(3\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(27\)
\(+\)\(+\)\(-\)\(-\)\(30\)
\(+\)\(-\)\(+\)\(-\)\(35\)
\(+\)\(-\)\(-\)\(+\)\(21\)
\(-\)\(+\)\(+\)\(-\)\(30\)
\(-\)\(+\)\(-\)\(+\)\(27\)
\(-\)\(-\)\(+\)\(+\)\(22\)
\(-\)\(-\)\(-\)\(-\)\(36\)
Plus space\(+\)\(97\)
Minus space\(-\)\(131\)

Trace form

\( 228q - 4q^{2} + 2q^{3} + 228q^{4} + 2q^{6} - 12q^{8} + 228q^{9} + O(q^{10}) \) \( 228q - 4q^{2} + 2q^{3} + 228q^{4} + 2q^{6} - 12q^{8} + 228q^{9} + 4q^{10} - 8q^{11} + 6q^{12} + 8q^{13} + 2q^{15} + 220q^{16} + 8q^{17} - 4q^{18} - 8q^{20} + 8q^{21} - 8q^{22} - 6q^{24} + 228q^{25} + 24q^{26} + 2q^{27} + 8q^{28} - 8q^{29} - 2q^{30} + 12q^{32} + 8q^{34} + 228q^{36} + 8q^{37} + 4q^{39} + 12q^{40} + 8q^{41} - 8q^{42} - 24q^{43} - 16q^{44} + 32q^{46} - 16q^{47} + 30q^{48} + 260q^{49} - 4q^{50} - 12q^{51} + 40q^{52} + 2q^{54} - 16q^{55} + 48q^{56} + 48q^{58} - 48q^{59} + 6q^{60} + 32q^{61} + 80q^{62} + 236q^{64} + 8q^{65} + 32q^{66} - 24q^{67} + 96q^{68} + 8q^{69} + 8q^{70} - 16q^{71} - 12q^{72} + 8q^{73} + 40q^{74} + 2q^{75} - 8q^{77} + 4q^{78} + 228q^{81} + 40q^{82} - 16q^{83} + 8q^{84} - 12q^{87} - 8q^{88} + 24q^{89} + 4q^{90} - 48q^{91} - 40q^{92} + 24q^{93} - 48q^{94} + 10q^{96} + 56q^{97} - 36q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5415))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 19
5415.2.a.a \(1\) \(43.239\) \(\Q\) None \(-2\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.b \(1\) \(43.239\) \(\Q\) None \(-2\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.c \(1\) \(43.239\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
5415.2.a.d \(1\) \(43.239\) \(\Q\) None \(-1\) \(1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5415.2.a.e \(1\) \(43.239\) \(\Q\) None \(-1\) \(1\) \(1\) \(4\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
5415.2.a.f \(1\) \(43.239\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(+\) \(-\) \(-\) \(q-q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
5415.2.a.g \(1\) \(43.239\) \(\Q\) None \(0\) \(1\) \(1\) \(2\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
5415.2.a.h \(1\) \(43.239\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
5415.2.a.i \(1\) \(43.239\) \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5415.2.a.j \(1\) \(43.239\) \(\Q\) None \(1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
5415.2.a.k \(1\) \(43.239\) \(\Q\) None \(2\) \(1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.l \(1\) \(43.239\) \(\Q\) None \(2\) \(1\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.m \(2\) \(43.239\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.n \(2\) \(43.239\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.o \(2\) \(43.239\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.p \(2\) \(43.239\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(4\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.q \(2\) \(43.239\) \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(-2\) \(6\) \(-\) \(+\) \(+\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
5415.2.a.r \(2\) \(43.239\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(-2\) \(+\) \(-\) \(-\) \(q+\beta q^{2}-q^{3}+q^{4}+q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.s \(2\) \(43.239\) \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(2\) \(-2\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+5q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.t \(2\) \(43.239\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(-2\) \(6\) \(+\) \(+\) \(-\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
5415.2.a.u \(2\) \(43.239\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.v \(2\) \(43.239\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.w \(3\) \(43.239\) 3.3.148.1 None \(-1\) \(3\) \(3\) \(-4\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5415.2.a.x \(3\) \(43.239\) 3.3.148.1 None \(1\) \(-3\) \(3\) \(-4\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5415.2.a.y \(5\) \(43.239\) 5.5.8797896.1 None \(-1\) \(-5\) \(5\) \(2\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.z \(5\) \(43.239\) 5.5.8797896.1 None \(1\) \(5\) \(5\) \(2\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.ba \(6\) \(43.239\) 6.6.966125.1 None \(-3\) \(-6\) \(6\) \(4\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{2})q^{2}-q^{3}+(2-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bb \(6\) \(43.239\) 6.6.1397493.1 None \(-3\) \(6\) \(6\) \(-6\) \(-\) \(-\) \(+\) \(q+(-\beta _{1}-\beta _{5})q^{2}+q^{3}+(\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bc \(6\) \(43.239\) 6.6.5061125.1 None \(-3\) \(6\) \(-6\) \(6\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5415.2.a.bd \(6\) \(43.239\) 6.6.2591125.1 None \(-1\) \(-6\) \(6\) \(2\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5415.2.a.be \(6\) \(43.239\) 6.6.5516125.1 None \(-1\) \(6\) \(-6\) \(4\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
5415.2.a.bf \(6\) \(43.239\) 6.6.5516125.1 None \(1\) \(-6\) \(-6\) \(4\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
5415.2.a.bg \(6\) \(43.239\) 6.6.2591125.1 None \(1\) \(6\) \(6\) \(2\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5415.2.a.bh \(6\) \(43.239\) 6.6.1397493.1 None \(3\) \(-6\) \(6\) \(-6\) \(+\) \(-\) \(-\) \(q+(\beta _{1}+\beta _{5})q^{2}-q^{3}+(\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bi \(6\) \(43.239\) 6.6.5061125.1 None \(3\) \(-6\) \(-6\) \(6\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bj \(6\) \(43.239\) 6.6.966125.1 None \(3\) \(6\) \(6\) \(4\) \(-\) \(-\) \(-\) \(q+(1-\beta _{2})q^{2}+q^{3}+(2-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
5415.2.a.bk \(9\) \(43.239\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(9\) \(-9\) \(-6\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
5415.2.a.bl \(9\) \(43.239\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(3\) \(-9\) \(-9\) \(-6\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
5415.2.a.bm \(12\) \(43.239\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-12\) \(-12\) \(-10\) \(+\) \(+\) \(+\) \(q+\beta _{9}q^{2}-q^{3}+(1+\beta _{7}-\beta _{9})q^{4}-q^{5}+\cdots\)
5415.2.a.bn \(12\) \(43.239\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(12\) \(12\) \(-6\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{8}+\beta _{9})q^{4}+q^{5}+\cdots\)
5415.2.a.bo \(12\) \(43.239\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-12\) \(-12\) \(6\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.bp \(12\) \(43.239\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(12\) \(-12\) \(6\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.bq \(12\) \(43.239\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(-12\) \(12\) \(-6\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{8}+\beta _{9})q^{4}+q^{5}+\cdots\)
5415.2.a.br \(12\) \(43.239\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(12\) \(-12\) \(-10\) \(-\) \(+\) \(+\) \(q-\beta _{9}q^{2}+q^{3}+(1+\beta _{7}-\beta _{9})q^{4}-q^{5}+\cdots\)
5415.2.a.bs \(15\) \(43.239\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-3\) \(-15\) \(15\) \(6\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.bt \(15\) \(43.239\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(3\) \(15\) \(15\) \(6\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5415))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5415)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\)\(^{\oplus 2}\)